Physics Book - User contributions [en]

Sinusoidal Electromagnetic Radiaton

2015-12-05T18:39:33Z

Ivierno3: /* Charge Moving Sinusoidally */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation emitted is sinusoidal?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 
<math>v_y=\frac{dy}{dt}=wymax\cos(wt)</math> <math>a_y=\frac{dv_y}{dt}=-w^2ymax\sin(wt)</math>

===Amplitude===
[[File:Amp.gif|left|500px|thumb|Finding amplitude]]
Amplitude is the height of the maximum peak during oscillation. As seen from the diagram, we only measure the distance from the x axis and do not include the area below the axis. The amplitude is also the maximum magnitude of the electric field.

===Period===
[[File:Period.jpg|thumb|200px|Finding period]]
The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle. As seen in the diagram, one cycle begins at 1 second and ends at 5 seconds. Thus the period of this graph would be four seconds.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by <math>f=\frac{w}{2pi}=\frac{1}{T}</math>.

===Wavelength===
[[File:Wavelength .jpg]]
 Wavelength is used to describe sinusoidal electromagnetic radiation. The wavelength is the distance between the 2 maximum points and thus is calculated by using speed of light and frequency. wavelength<math>=cT</math> and <math>T=\frac{1}{f}</math>
 Electromagnetic radiation of different wavelengths have different names such as x-ray or microwaves. Radiation with certain wavelengths also possess certain qualities such as wavelengths of 400nm to 700nm are known as visible light as they can be seen by the human eye.

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is wavelength over period.
#Another way is by timing the arrival of the radiative electric field, which would be distance over change of time.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space when light wave has to travel through water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength. The image shows how different things are categorized based on wavelength.
[[File:Spectrum123.jpg]]

===A Computational Model===

Visit the link to below to observe how amplitude and frequency affects sinusoidal waves and the direction of speed.
https://phet.colorado.edu/sims/radiating-charge/radiating-charge_en.html

==Examples==

Calculate the wavelength of a radio which has 1380 kiloHertz.

First convert kilohertz to Hertz by <math>1380*1000=1380000</math>
Secondly wavelength is speed of light over frequency so <math>\frac{3e8}{1380000}=217.39m</math>

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

For an understanding on radiative electric field readers should first read http://www.physicsbook.gatech.edu/Producing_a_Radiative_Electric_Field 
For further information on wavelengths and frequency http://www.physicsbook.gatech.edu/Wavelength_and_Frequency

===Further reading===

Books, Articles or other print media on this topic

===External links===

http://physics.tutorvista.com/waves/wave-frequency.html
http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-3-Biology-Vol-1/Electromagnetic-Spectrum-Real-life-applications.html
http://www.pstcc.edu/departments/natural_behavioral_sciences/Web%20Physics/Chapter016.htm

==References==

http://www.tapir.caltech.edu/~teviet/Waves/empulse.html
http://physics.tutorvista.com/waves/wave-frequency.html
http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-3-Biology-Vol-1/Electromagnetic-Spectrum-Real-life-applications.html
http://www.pstcc.edu/departments/natural_behavioral_sciences/Web%20Physics/Chapter016.htm

[[Category:Which Category did you place this in?]]

Sinusoidal Electromagnetic Radiaton

2015-12-05T18:37:31Z

Ivierno3: /* Examples */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation also be be emitted sinusoidally?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 
<math>v_y=\frac{dy}{dt}=wymax\cos(wt)</math> <math>a_y=\frac{dv_y}{dt}=-w^2ymax\sin(wt)</math>

===Amplitude===
[[File:Amp.gif|left|500px|thumb|Finding amplitude]]
Amplitude is the height of the maximum peak during oscillation. As seen from the diagram, we only measure the distance from the x axis and do not include the area below the axis. The amplitude is also the maximum magnitude of the electric field.

===Period===
[[File:Period.jpg|thumb|200px|Finding period]]
The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle. As seen in the diagram, one cycle begins at 1 second and ends at 5 seconds. Thus the period of this graph would be four seconds.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by <math>f=\frac{w}{2pi}=\frac{1}{T}</math>.

===Wavelength===
[[File:Wavelength .jpg]]
 Wavelength is used to describe sinusoidal electromagnetic radiation. The wavelength is the distance between the 2 maximum points and thus is calculated by using speed of light and frequency. wavelength<math>=cT</math> and <math>T=\frac{1}{f}</math>
 Electromagnetic radiation of different wavelengths have different names such as x-ray or microwaves. Radiation with certain wavelengths also possess certain qualities such as wavelengths of 400nm to 700nm are known as visible light as they can be seen by the human eye.

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is wavelength over period.
#Another way is by timing the arrival of the radiative electric field, which would be distance over change of time.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space when light wave has to travel through water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength. The image shows how different things are categorized based on wavelength.
[[File:Spectrum123.jpg]]

===A Computational Model===

Visit the link to below to observe how amplitude and frequency affects sinusoidal waves and the direction of speed.
https://phet.colorado.edu/sims/radiating-charge/radiating-charge_en.html

==Examples==

Calculate the wavelength of a radio which has 1380 kiloHertz.

First convert kilohertz to Hertz by <math>1380*1000=1380000</math>
Secondly wavelength is speed of light over frequency so <math>\frac{3e8}{1380000}=217.39m</math>

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

For an understanding on radiative electric field readers should first read http://www.physicsbook.gatech.edu/Producing_a_Radiative_Electric_Field 
For further information on wavelengths and frequency http://www.physicsbook.gatech.edu/Wavelength_and_Frequency

===Further reading===

Books, Articles or other print media on this topic

===External links===

http://physics.tutorvista.com/waves/wave-frequency.html
http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-3-Biology-Vol-1/Electromagnetic-Spectrum-Real-life-applications.html
http://www.pstcc.edu/departments/natural_behavioral_sciences/Web%20Physics/Chapter016.htm

==References==

http://www.tapir.caltech.edu/~teviet/Waves/empulse.html
http://physics.tutorvista.com/waves/wave-frequency.html
http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-3-Biology-Vol-1/Electromagnetic-Spectrum-Real-life-applications.html
http://www.pstcc.edu/departments/natural_behavioral_sciences/Web%20Physics/Chapter016.htm

[[Category:Which Category did you place this in?]]

Sinusoidal Electromagnetic Radiaton

2015-12-05T18:37:03Z

Ivierno3: /* Simple */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation also be be emitted sinusoidally?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 
<math>v_y=\frac{dy}{dt}=wymax\cos(wt)</math> <math>a_y=\frac{dv_y}{dt}=-w^2ymax\sin(wt)</math>

===Amplitude===
[[File:Amp.gif|left|500px|thumb|Finding amplitude]]
Amplitude is the height of the maximum peak during oscillation. As seen from the diagram, we only measure the distance from the x axis and do not include the area below the axis. The amplitude is also the maximum magnitude of the electric field.

===Period===
[[File:Period.jpg|thumb|200px|Finding period]]
The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle. As seen in the diagram, one cycle begins at 1 second and ends at 5 seconds. Thus the period of this graph would be four seconds.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by <math>f=\frac{w}{2pi}=\frac{1}{T}</math>.

===Wavelength===
[[File:Wavelength .jpg]]
 Wavelength is used to describe sinusoidal electromagnetic radiation. The wavelength is the distance between the 2 maximum points and thus is calculated by using speed of light and frequency. wavelength<math>=cT</math> and <math>T=\frac{1}{f}</math>
 Electromagnetic radiation of different wavelengths have different names such as x-ray or microwaves. Radiation with certain wavelengths also possess certain qualities such as wavelengths of 400nm to 700nm are known as visible light as they can be seen by the human eye.

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is wavelength over period.
#Another way is by timing the arrival of the radiative electric field, which would be distance over change of time.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space when light wave has to travel through water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength. The image shows how different things are categorized based on wavelength.
[[File:Spectrum123.jpg]]

===A Computational Model===

Visit the link to below to observe how amplitude and frequency affects sinusoidal waves and the direction of speed.
https://phet.colorado.edu/sims/radiating-charge/radiating-charge_en.html

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Calculate the wavelength of a radio which has 1380 kiloHertz.

First convert kilohertz to Hertz by <math>1380*1000=1380000</math>
Secondly wavelength is speed of light over frequency so <math>\frac{3e8}{1380000}=217.39m</math>

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

For an understanding on radiative electric field readers should first read http://www.physicsbook.gatech.edu/Producing_a_Radiative_Electric_Field 
For further information on wavelengths and frequency http://www.physicsbook.gatech.edu/Wavelength_and_Frequency

===Further reading===

Books, Articles or other print media on this topic

===External links===

http://physics.tutorvista.com/waves/wave-frequency.html
http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-3-Biology-Vol-1/Electromagnetic-Spectrum-Real-life-applications.html
http://www.pstcc.edu/departments/natural_behavioral_sciences/Web%20Physics/Chapter016.htm

==References==

http://www.tapir.caltech.edu/~teviet/Waves/empulse.html
http://physics.tutorvista.com/waves/wave-frequency.html
http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-3-Biology-Vol-1/Electromagnetic-Spectrum-Real-life-applications.html
http://www.pstcc.edu/departments/natural_behavioral_sciences/Web%20Physics/Chapter016.htm

[[Category:Which Category did you place this in?]]

Sinusoidal Electromagnetic Radiaton

2015-12-05T18:36:36Z

Ivierno3: /* Simple */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation also be be emitted sinusoidally?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 
<math>v_y=\frac{dy}{dt}=wymax\cos(wt)</math> <math>a_y=\frac{dv_y}{dt}=-w^2ymax\sin(wt)</math>

===Amplitude===
[[File:Amp.gif|left|500px|thumb|Finding amplitude]]
Amplitude is the height of the maximum peak during oscillation. As seen from the diagram, we only measure the distance from the x axis and do not include the area below the axis. The amplitude is also the maximum magnitude of the electric field.

===Period===
[[File:Period.jpg|thumb|200px|Finding period]]
The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle. As seen in the diagram, one cycle begins at 1 second and ends at 5 seconds. Thus the period of this graph would be four seconds.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by <math>f=\frac{w}{2pi}=\frac{1}{T}</math>.

===Wavelength===
[[File:Wavelength .jpg]]
 Wavelength is used to describe sinusoidal electromagnetic radiation. The wavelength is the distance between the 2 maximum points and thus is calculated by using speed of light and frequency. wavelength<math>=cT</math> and <math>T=\frac{1}{f}</math>
 Electromagnetic radiation of different wavelengths have different names such as x-ray or microwaves. Radiation with certain wavelengths also possess certain qualities such as wavelengths of 400nm to 700nm are known as visible light as they can be seen by the human eye.

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is wavelength over period.
#Another way is by timing the arrival of the radiative electric field, which would be distance over change of time.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space when light wave has to travel through water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength. The image shows how different things are categorized based on wavelength.
[[File:Spectrum123.jpg]]

===A Computational Model===

Visit the link to below to observe how amplitude and frequency affects sinusoidal waves and the direction of speed.
https://phet.colorado.edu/sims/radiating-charge/radiating-charge_en.html

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Calculate the wavelength of a radio which has 1380 kiloHertz.

First convert kilohertz to Hertz by <math>1380*1000=1380000</math>
Secondly wavelength is speed of light over frequency so <math>\frac{3e8}{1380000}=217.39m

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

For an understanding on radiative electric field readers should first read http://www.physicsbook.gatech.edu/Producing_a_Radiative_Electric_Field 
For further information on wavelengths and frequency http://www.physicsbook.gatech.edu/Wavelength_and_Frequency

===Further reading===

Books, Articles or other print media on this topic

===External links===

http://physics.tutorvista.com/waves/wave-frequency.html
http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-3-Biology-Vol-1/Electromagnetic-Spectrum-Real-life-applications.html
http://www.pstcc.edu/departments/natural_behavioral_sciences/Web%20Physics/Chapter016.htm

==References==

http://www.tapir.caltech.edu/~teviet/Waves/empulse.html
http://physics.tutorvista.com/waves/wave-frequency.html
http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-3-Biology-Vol-1/Electromagnetic-Spectrum-Real-life-applications.html
http://www.pstcc.edu/departments/natural_behavioral_sciences/Web%20Physics/Chapter016.htm

[[Category:Which Category did you place this in?]]

Sinusoidal Electromagnetic Radiaton

2015-12-05T18:32:25Z

Ivierno3: /* Electromagnetic Spectrum */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation also be be emitted sinusoidally?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 
<math>v_y=\frac{dy}{dt}=wymax\cos(wt)</math> <math>a_y=\frac{dv_y}{dt}=-w^2ymax\sin(wt)</math>

===Amplitude===
[[File:Amp.gif|left|500px|thumb|Finding amplitude]]
Amplitude is the height of the maximum peak during oscillation. As seen from the diagram, we only measure the distance from the x axis and do not include the area below the axis. The amplitude is also the maximum magnitude of the electric field.

===Period===
[[File:Period.jpg|thumb|200px|Finding period]]
The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle. As seen in the diagram, one cycle begins at 1 second and ends at 5 seconds. Thus the period of this graph would be four seconds.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by <math>f=\frac{w}{2pi}=\frac{1}{T}</math>.

===Wavelength===
[[File:Wavelength .jpg]]
 Wavelength is used to describe sinusoidal electromagnetic radiation. The wavelength is the distance between the 2 maximum points and thus is calculated by using speed of light and frequency. wavelength<math>=cT</math> and <math>T=\frac{1}{f}</math>
 Electromagnetic radiation of different wavelengths have different names such as x-ray or microwaves. Radiation with certain wavelengths also possess certain qualities such as wavelengths of 400nm to 700nm are known as visible light as they can be seen by the human eye.

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is wavelength over period.
#Another way is by timing the arrival of the radiative electric field, which would be distance over change of time.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space when light wave has to travel through water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength. The image shows how different things are categorized based on wavelength.
[[File:Spectrum123.jpg]]

===A Computational Model===

Visit the link to below to observe how amplitude and frequency affects sinusoidal waves and the direction of speed.
https://phet.colorado.edu/sims/radiating-charge/radiating-charge_en.html

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Show that the electromagnetic radiation emitted is sinusoidally when the charge is moving sinusoidally.

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

For an understanding on radiative electric field readers should first read http://www.physicsbook.gatech.edu/Producing_a_Radiative_Electric_Field 
For further information on wavelengths and frequency http://www.physicsbook.gatech.edu/Wavelength_and_Frequency

===Further reading===

Books, Articles or other print media on this topic

===External links===

http://physics.tutorvista.com/waves/wave-frequency.html
http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-3-Biology-Vol-1/Electromagnetic-Spectrum-Real-life-applications.html
http://www.pstcc.edu/departments/natural_behavioral_sciences/Web%20Physics/Chapter016.htm

==References==

http://www.tapir.caltech.edu/~teviet/Waves/empulse.html
http://physics.tutorvista.com/waves/wave-frequency.html
http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-3-Biology-Vol-1/Electromagnetic-Spectrum-Real-life-applications.html
http://www.pstcc.edu/departments/natural_behavioral_sciences/Web%20Physics/Chapter016.htm

[[Category:Which Category did you place this in?]]

File:Spectrum123.jpg

2015-12-05T18:32:05Z

Ivierno3:

Sinusoidal Electromagnetic Radiaton

2015-12-05T18:31:34Z

Ivierno3: /* Electromagnetic Spectrum */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation also be be emitted sinusoidally?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 
<math>v_y=\frac{dy}{dt}=wymax\cos(wt)</math> <math>a_y=\frac{dv_y}{dt}=-w^2ymax\sin(wt)</math>

===Amplitude===
[[File:Amp.gif|left|500px|thumb|Finding amplitude]]
Amplitude is the height of the maximum peak during oscillation. As seen from the diagram, we only measure the distance from the x axis and do not include the area below the axis. The amplitude is also the maximum magnitude of the electric field.

===Period===
[[File:Period.jpg|thumb|200px|Finding period]]
The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle. As seen in the diagram, one cycle begins at 1 second and ends at 5 seconds. Thus the period of this graph would be four seconds.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by <math>f=\frac{w}{2pi}=\frac{1}{T}</math>.

===Wavelength===
[[File:Wavelength .jpg]]
 Wavelength is used to describe sinusoidal electromagnetic radiation. The wavelength is the distance between the 2 maximum points and thus is calculated by using speed of light and frequency. wavelength<math>=cT</math> and <math>T=\frac{1}{f}</math>
 Electromagnetic radiation of different wavelengths have different names such as x-ray or microwaves. Radiation with certain wavelengths also possess certain qualities such as wavelengths of 400nm to 700nm are known as visible light as they can be seen by the human eye.

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is wavelength over period.
#Another way is by timing the arrival of the radiative electric field, which would be distance over change of time.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space when light wave has to travel through water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength. The image shows how different things are categorized based on wavelength.
[[File:spectrum123.jpg]]

===A Computational Model===

Visit the link to below to observe how amplitude and frequency affects sinusoidal waves and the direction of speed.
https://phet.colorado.edu/sims/radiating-charge/radiating-charge_en.html

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Show that the electromagnetic radiation emitted is sinusoidally when the charge is moving sinusoidally.

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

For an understanding on radiative electric field readers should first read http://www.physicsbook.gatech.edu/Producing_a_Radiative_Electric_Field 
For further information on wavelengths and frequency http://www.physicsbook.gatech.edu/Wavelength_and_Frequency

===Further reading===

Books, Articles or other print media on this topic

===External links===

http://physics.tutorvista.com/waves/wave-frequency.html
http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-3-Biology-Vol-1/Electromagnetic-Spectrum-Real-life-applications.html
http://www.pstcc.edu/departments/natural_behavioral_sciences/Web%20Physics/Chapter016.htm

==References==

http://www.tapir.caltech.edu/~teviet/Waves/empulse.html
http://physics.tutorvista.com/waves/wave-frequency.html
http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-3-Biology-Vol-1/Electromagnetic-Spectrum-Real-life-applications.html
http://www.pstcc.edu/departments/natural_behavioral_sciences/Web%20Physics/Chapter016.htm

[[Category:Which Category did you place this in?]]

Sinusoidal Electromagnetic Radiaton

2015-12-05T18:30:33Z

Ivierno3: /* Electromagnetic Spectrum */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation also be be emitted sinusoidally?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 
<math>v_y=\frac{dy}{dt}=wymax\cos(wt)</math> <math>a_y=\frac{dv_y}{dt}=-w^2ymax\sin(wt)</math>

===Amplitude===
[[File:Amp.gif|left|500px|thumb|Finding amplitude]]
Amplitude is the height of the maximum peak during oscillation. As seen from the diagram, we only measure the distance from the x axis and do not include the area below the axis. The amplitude is also the maximum magnitude of the electric field.

===Period===
[[File:Period.jpg|thumb|200px|Finding period]]
The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle. As seen in the diagram, one cycle begins at 1 second and ends at 5 seconds. Thus the period of this graph would be four seconds.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by <math>f=\frac{w}{2pi}=\frac{1}{T}</math>.

===Wavelength===
[[File:Wavelength .jpg]]
 Wavelength is used to describe sinusoidal electromagnetic radiation. The wavelength is the distance between the 2 maximum points and thus is calculated by using speed of light and frequency. wavelength<math>=cT</math> and <math>T=\frac{1}{f}</math>
 Electromagnetic radiation of different wavelengths have different names such as x-ray or microwaves. Radiation with certain wavelengths also possess certain qualities such as wavelengths of 400nm to 700nm are known as visible light as they can be seen by the human eye.

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is wavelength over period.
#Another way is by timing the arrival of the radiative electric field, which would be distance over change of time.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space when light wave has to travel through water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength. The image shows how different things are categorized based on wavelength.
[[File:spectrum.jpg]]

===A Computational Model===

Visit the link to below to observe how amplitude and frequency affects sinusoidal waves and the direction of speed.
https://phet.colorado.edu/sims/radiating-charge/radiating-charge_en.html

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Show that the electromagnetic radiation emitted is sinusoidally when the charge is moving sinusoidally.

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

For an understanding on radiative electric field readers should first read http://www.physicsbook.gatech.edu/Producing_a_Radiative_Electric_Field 
For further information on wavelengths and frequency http://www.physicsbook.gatech.edu/Wavelength_and_Frequency

===Further reading===

Books, Articles or other print media on this topic

===External links===

http://physics.tutorvista.com/waves/wave-frequency.html
http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-3-Biology-Vol-1/Electromagnetic-Spectrum-Real-life-applications.html
http://www.pstcc.edu/departments/natural_behavioral_sciences/Web%20Physics/Chapter016.htm

==References==

http://www.tapir.caltech.edu/~teviet/Waves/empulse.html
http://physics.tutorvista.com/waves/wave-frequency.html
http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-3-Biology-Vol-1/Electromagnetic-Spectrum-Real-life-applications.html
http://www.pstcc.edu/departments/natural_behavioral_sciences/Web%20Physics/Chapter016.htm

[[Category:Which Category did you place this in?]]

Sinusoidal Electromagnetic Radiaton

2015-12-05T18:28:27Z

Ivierno3: /* Speed */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation also be be emitted sinusoidally?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 
<math>v_y=\frac{dy}{dt}=wymax\cos(wt)</math> <math>a_y=\frac{dv_y}{dt}=-w^2ymax\sin(wt)</math>

===Amplitude===
[[File:Amp.gif|left|500px|thumb|Finding amplitude]]
Amplitude is the height of the maximum peak during oscillation. As seen from the diagram, we only measure the distance from the x axis and do not include the area below the axis. The amplitude is also the maximum magnitude of the electric field.

===Period===
[[File:Period.jpg|thumb|200px|Finding period]]
The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle. As seen in the diagram, one cycle begins at 1 second and ends at 5 seconds. Thus the period of this graph would be four seconds.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by <math>f=\frac{w}{2pi}=\frac{1}{T}</math>.

===Wavelength===
[[File:Wavelength .jpg]]
 Wavelength is used to describe sinusoidal electromagnetic radiation. The wavelength is the distance between the 2 maximum points and thus is calculated by using speed of light and frequency. wavelength<math>=cT</math> and <math>T=\frac{1}{f}</math>
 Electromagnetic radiation of different wavelengths have different names such as x-ray or microwaves. Radiation with certain wavelengths also possess certain qualities such as wavelengths of 400nm to 700nm are known as visible light as they can be seen by the human eye.

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is wavelength over period.
#Another way is by timing the arrival of the radiative electric field, which would be distance over change of time.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space when light wave has to travel through water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength.

===A Computational Model===

Visit the link to below to observe how amplitude and frequency affects sinusoidal waves and the direction of speed.
https://phet.colorado.edu/sims/radiating-charge/radiating-charge_en.html

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Show that the electromagnetic radiation emitted is sinusoidally when the charge is moving sinusoidally.

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

For an understanding on radiative electric field readers should first read http://www.physicsbook.gatech.edu/Producing_a_Radiative_Electric_Field 
For further information on wavelengths and frequency http://www.physicsbook.gatech.edu/Wavelength_and_Frequency

===Further reading===

Books, Articles or other print media on this topic

===External links===

http://physics.tutorvista.com/waves/wave-frequency.html
http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-3-Biology-Vol-1/Electromagnetic-Spectrum-Real-life-applications.html
http://www.pstcc.edu/departments/natural_behavioral_sciences/Web%20Physics/Chapter016.htm

==References==

http://www.tapir.caltech.edu/~teviet/Waves/empulse.html
http://physics.tutorvista.com/waves/wave-frequency.html
http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-3-Biology-Vol-1/Electromagnetic-Spectrum-Real-life-applications.html
http://www.pstcc.edu/departments/natural_behavioral_sciences/Web%20Physics/Chapter016.htm

[[Category:Which Category did you place this in?]]

Sinusoidal Electromagnetic Radiaton

2015-12-05T18:22:12Z

Ivierno3: /* A Computational Model */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation also be be emitted sinusoidally?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 
<math>v_y=\frac{dy}{dt}=wymax\cos(wt)</math> <math>a_y=\frac{dv_y}{dt}=-w^2ymax\sin(wt)</math>

===Amplitude===
[[File:Amp.gif|left|500px|thumb|Finding amplitude]]
Amplitude is the height of the maximum peak during oscillation. As seen from the diagram, we only measure the distance from the x axis and do not include the area below the axis. The amplitude is also the maximum magnitude of the electric field.

===Period===
[[File:Period.jpg|thumb|200px|Finding period]]
The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle. As seen in the diagram, one cycle begins at 1 second and ends at 5 seconds. Thus the period of this graph would be four seconds.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by <math>f=\frac{w}{2pi}=\frac{1}{T}</math>.

===Wavelength===
[[File:Wavelength .jpg]]
 Wavelength is used to describe sinusoidal electromagnetic radiation. The wavelength is the distance between the 2 maximum points and thus is calculated by using speed of light and frequency. wavelength<math>=cT</math> and <math>T=\frac{1}{f}</math>
 Electromagnetic radiation of different wavelengths have different names such as x-ray or microwaves. Radiation with certain wavelengths also possess certain qualities such as wavelengths of 400nm to 700nm are known as visible light as they can be seen by the human eye.

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is
#Another way is using the it of the arrival of the radiative electric field.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space through which light wave has to travel to water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength.

===A Computational Model===

Visit the link to below to observe how amplitude and frequency affects sinusoidal waves and the direction of speed.
https://phet.colorado.edu/sims/radiating-charge/radiating-charge_en.html

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Show that the electromagnetic radiation emitted is sinusoidally when the charge is moving sinusoidally.

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

For an understanding on radiative electric field readers should first read http://www.physicsbook.gatech.edu/Producing_a_Radiative_Electric_Field 
For further information on wavelengths and frequency http://www.physicsbook.gatech.edu/Wavelength_and_Frequency

===Further reading===

Books, Articles or other print media on this topic

===External links===

http://physics.tutorvista.com/waves/wave-frequency.html
http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-3-Biology-Vol-1/Electromagnetic-Spectrum-Real-life-applications.html
http://www.pstcc.edu/departments/natural_behavioral_sciences/Web%20Physics/Chapter016.htm

==References==

http://www.tapir.caltech.edu/~teviet/Waves/empulse.html
http://physics.tutorvista.com/waves/wave-frequency.html
http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-3-Biology-Vol-1/Electromagnetic-Spectrum-Real-life-applications.html
http://www.pstcc.edu/departments/natural_behavioral_sciences/Web%20Physics/Chapter016.htm

[[Category:Which Category did you place this in?]]

Sinusoidal Electromagnetic Radiaton

2015-12-05T18:15:02Z

Ivierno3: /* A Mathematical Model */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation also be be emitted sinusoidally?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 
<math>v_y=\frac{dy}{dt}=wymax\cos(wt)</math> <math>a_y=\frac{dv_y}{dt}=-w^2ymax\sin(wt)</math>

===Amplitude===
[[File:Amp.gif|left|500px|thumb|Finding amplitude]]
Amplitude is the height of the maximum peak during oscillation. As seen from the diagram, we only measure the distance from the x axis and do not include the area below the axis. The amplitude is also the maximum magnitude of the electric field.

===Period===
[[File:Period.jpg|thumb|200px|Finding period]]
The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle. As seen in the diagram, one cycle begins at 1 second and ends at 5 seconds. Thus the period of this graph would be four seconds.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by <math>f=\frac{w}{2pi}=\frac{1}{T}</math>.

===Wavelength===
[[File:Wavelength .jpg]]
 Wavelength is used to describe sinusoidal electromagnetic radiation. The wavelength is the distance between the 2 maximum points and thus is calculated by using speed of light and frequency. wavelength<math>=cT</math> and <math>T=\frac{1}{f}</math>
 Electromagnetic radiation of different wavelengths have different names such as x-ray or microwaves. Radiation with certain wavelengths also possess certain qualities such as wavelengths of 400nm to 700nm are known as visible light as they can be seen by the human eye.

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is
#Another way is using the it of the arrival of the radiative electric field.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space through which light wave has to travel to water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Show that the electromagnetic radiation emitted is sinusoidally when the charge is moving sinusoidally.

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

For an understanding on radiative electric field readers should first read http://www.physicsbook.gatech.edu/Producing_a_Radiative_Electric_Field 
For further information on wavelengths and frequency http://www.physicsbook.gatech.edu/Wavelength_and_Frequency

===Further reading===

Books, Articles or other print media on this topic

===External links===

http://physics.tutorvista.com/waves/wave-frequency.html
http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-3-Biology-Vol-1/Electromagnetic-Spectrum-Real-life-applications.html
http://www.pstcc.edu/departments/natural_behavioral_sciences/Web%20Physics/Chapter016.htm

==References==

http://www.tapir.caltech.edu/~teviet/Waves/empulse.html
http://physics.tutorvista.com/waves/wave-frequency.html
http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-3-Biology-Vol-1/Electromagnetic-Spectrum-Real-life-applications.html
http://www.pstcc.edu/departments/natural_behavioral_sciences/Web%20Physics/Chapter016.htm

[[Category:Which Category did you place this in?]]

Sinusoidal Electromagnetic Radiaton

2015-12-05T18:14:32Z

Ivierno3: /* See also */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation also be be emitted sinusoidally?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 
<math>v_y=\frac{dy}{dt}=wymax\cos(wt)</math> <math>a_y=\frac{dv_y}{dt}=-w^2ymax\sin(wt)</math>

===Amplitude===
[[File:Amp.gif|left|500px|thumb|Finding amplitude]]
Amplitude is the height of the maximum peak during oscillation. As seen from the diagram, we only measure the distance from the x axis and do not include the area below the axis. The amplitude is also the maximum magnitude of the electric field.

===Period===
[[File:Period.jpg|thumb|200px|Finding period]]
The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle. As seen in the diagram, one cycle begins at 1 second and ends at 5 seconds. Thus the period of this graph would be four seconds.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by <math>f=\frac{w}{2pi}=\frac{1}{T}</math>.

===Wavelength===
[[File:Wavelength .jpg]]
 Wavelength is used to describe sinusoidal electromagnetic radiation. The wavelength is the distance between the 2 maximum points and thus is calculated by using speed of light and frequency. wavelength<math>=cT</math> and <math>T=\frac{1}{f}</math>
 Electromagnetic radiation of different wavelengths have different names such as x-ray or microwaves. Radiation with certain wavelengths also possess certain qualities such as wavelengths of 400nm to 700nm are known as visible light as they can be seen by the human eye.

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is
#Another way is using the it of the arrival of the radiative electric field.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space through which light wave has to travel to water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength.

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Show that the electromagnetic radiation emitted is sinusoidally when the charge is moving sinusoidally.

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

For an understanding on radiative electric field readers should first read http://www.physicsbook.gatech.edu/Producing_a_Radiative_Electric_Field 
For further information on wavelengths and frequency http://www.physicsbook.gatech.edu/Wavelength_and_Frequency

===Further reading===

Books, Articles or other print media on this topic

===External links===

http://physics.tutorvista.com/waves/wave-frequency.html
http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-3-Biology-Vol-1/Electromagnetic-Spectrum-Real-life-applications.html
http://www.pstcc.edu/departments/natural_behavioral_sciences/Web%20Physics/Chapter016.htm

==References==

http://www.tapir.caltech.edu/~teviet/Waves/empulse.html
http://physics.tutorvista.com/waves/wave-frequency.html
http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-3-Biology-Vol-1/Electromagnetic-Spectrum-Real-life-applications.html
http://www.pstcc.edu/departments/natural_behavioral_sciences/Web%20Physics/Chapter016.htm

[[Category:Which Category did you place this in?]]

Sinusoidal Electromagnetic Radiaton

2015-12-05T18:14:19Z

Ivierno3: /* See also */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation also be be emitted sinusoidally?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 
<math>v_y=\frac{dy}{dt}=wymax\cos(wt)</math> <math>a_y=\frac{dv_y}{dt}=-w^2ymax\sin(wt)</math>

===Amplitude===
[[File:Amp.gif|left|500px|thumb|Finding amplitude]]
Amplitude is the height of the maximum peak during oscillation. As seen from the diagram, we only measure the distance from the x axis and do not include the area below the axis. The amplitude is also the maximum magnitude of the electric field.

===Period===
[[File:Period.jpg|thumb|200px|Finding period]]
The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle. As seen in the diagram, one cycle begins at 1 second and ends at 5 seconds. Thus the period of this graph would be four seconds.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by <math>f=\frac{w}{2pi}=\frac{1}{T}</math>.

===Wavelength===
[[File:Wavelength .jpg]]
 Wavelength is used to describe sinusoidal electromagnetic radiation. The wavelength is the distance between the 2 maximum points and thus is calculated by using speed of light and frequency. wavelength<math>=cT</math> and <math>T=\frac{1}{f}</math>
 Electromagnetic radiation of different wavelengths have different names such as x-ray or microwaves. Radiation with certain wavelengths also possess certain qualities such as wavelengths of 400nm to 700nm are known as visible light as they can be seen by the human eye.

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is
#Another way is using the it of the arrival of the radiative electric field.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space through which light wave has to travel to water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength.

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Show that the electromagnetic radiation emitted is sinusoidally when the charge is moving sinusoidally.

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

For an understanding on radiative electric field readers should first read http://www.physicsbook.gatech.edu/Producing_a_Radiative_Electric_Field
For further information on wavelengths and frequency http://www.physicsbook.gatech.edu/Wavelength_and_Frequency

===Further reading===

Books, Articles or other print media on this topic

===External links===

http://physics.tutorvista.com/waves/wave-frequency.html
http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-3-Biology-Vol-1/Electromagnetic-Spectrum-Real-life-applications.html
http://www.pstcc.edu/departments/natural_behavioral_sciences/Web%20Physics/Chapter016.htm

==References==

http://www.tapir.caltech.edu/~teviet/Waves/empulse.html
http://physics.tutorvista.com/waves/wave-frequency.html
http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-3-Biology-Vol-1/Electromagnetic-Spectrum-Real-life-applications.html
http://www.pstcc.edu/departments/natural_behavioral_sciences/Web%20Physics/Chapter016.htm

[[Category:Which Category did you place this in?]]

Sinusoidal Electromagnetic Radiaton

2015-12-05T18:11:07Z

Ivierno3: /* References */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation also be be emitted sinusoidally?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 
<math>v_y=\frac{dy}{dt}=wymax\cos(wt)</math> <math>a_y=\frac{dv_y}{dt}=-w^2ymax\sin(wt)</math>

===Amplitude===
[[File:Amp.gif|left|500px|thumb|Finding amplitude]]
Amplitude is the height of the maximum peak during oscillation. As seen from the diagram, we only measure the distance from the x axis and do not include the area below the axis. The amplitude is also the maximum magnitude of the electric field.

===Period===
[[File:Period.jpg|thumb|200px|Finding period]]
The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle. As seen in the diagram, one cycle begins at 1 second and ends at 5 seconds. Thus the period of this graph would be four seconds.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by <math>f=\frac{w}{2pi}=\frac{1}{T}</math>.

===Wavelength===
[[File:Wavelength .jpg]]
 Wavelength is used to describe sinusoidal electromagnetic radiation. The wavelength is the distance between the 2 maximum points and thus is calculated by using speed of light and frequency. wavelength<math>=cT</math> and <math>T=\frac{1}{f}</math>
 Electromagnetic radiation of different wavelengths have different names such as x-ray or microwaves. Radiation with certain wavelengths also possess certain qualities such as wavelengths of 400nm to 700nm are known as visible light as they can be seen by the human eye.

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is
#Another way is using the it of the arrival of the radiative electric field.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space through which light wave has to travel to water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength.

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Show that the electromagnetic radiation emitted is sinusoidally when the charge is moving sinusoidally.

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

http://physics.tutorvista.com/waves/wave-frequency.html
http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-3-Biology-Vol-1/Electromagnetic-Spectrum-Real-life-applications.html
http://www.pstcc.edu/departments/natural_behavioral_sciences/Web%20Physics/Chapter016.htm

==References==

http://www.tapir.caltech.edu/~teviet/Waves/empulse.html
http://physics.tutorvista.com/waves/wave-frequency.html
http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-3-Biology-Vol-1/Electromagnetic-Spectrum-Real-life-applications.html
http://www.pstcc.edu/departments/natural_behavioral_sciences/Web%20Physics/Chapter016.htm

[[Category:Which Category did you place this in?]]

Sinusoidal Electromagnetic Radiaton

2015-12-05T18:10:47Z

Ivierno3: /* References */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation also be be emitted sinusoidally?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 
<math>v_y=\frac{dy}{dt}=wymax\cos(wt)</math> <math>a_y=\frac{dv_y}{dt}=-w^2ymax\sin(wt)</math>

===Amplitude===
[[File:Amp.gif|left|500px|thumb|Finding amplitude]]
Amplitude is the height of the maximum peak during oscillation. As seen from the diagram, we only measure the distance from the x axis and do not include the area below the axis. The amplitude is also the maximum magnitude of the electric field.

===Period===
[[File:Period.jpg|thumb|200px|Finding period]]
The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle. As seen in the diagram, one cycle begins at 1 second and ends at 5 seconds. Thus the period of this graph would be four seconds.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by <math>f=\frac{w}{2pi}=\frac{1}{T}</math>.

===Wavelength===
[[File:Wavelength .jpg]]
 Wavelength is used to describe sinusoidal electromagnetic radiation. The wavelength is the distance between the 2 maximum points and thus is calculated by using speed of light and frequency. wavelength<math>=cT</math> and <math>T=\frac{1}{f}</math>
 Electromagnetic radiation of different wavelengths have different names such as x-ray or microwaves. Radiation with certain wavelengths also possess certain qualities such as wavelengths of 400nm to 700nm are known as visible light as they can be seen by the human eye.

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is
#Another way is using the it of the arrival of the radiative electric field.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space through which light wave has to travel to water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength.

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Show that the electromagnetic radiation emitted is sinusoidally when the charge is moving sinusoidally.

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

http://physics.tutorvista.com/waves/wave-frequency.html
http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-3-Biology-Vol-1/Electromagnetic-Spectrum-Real-life-applications.html
http://www.pstcc.edu/departments/natural_behavioral_sciences/Web%20Physics/Chapter016.htm

==References==

http://www.tapir.caltech.edu/~teviet/Waves/empulse.html https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&ved=0ahUKEwiryKbZ48HJAhXEQyYKHfKpArQQjRwIBw&url=http%3A%2F%2Fwww.edn.com%2FHome%2FPrintView%3FcontentItemId%3D4018934&psig=AFQjCNFhkmO6iOffgv1gXiFATzPxD151Xw&ust=1449303838812175
http://physics.tutorvista.com/waves/wave-frequency.html
http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-3-Biology-Vol-1/Electromagnetic-Spectrum-Real-life-applications.html
http://www.pstcc.edu/departments/natural_behavioral_sciences/Web%20Physics/Chapter016.htm

[[Category:Which Category did you place this in?]]

Sinusoidal Electromagnetic Radiaton

2015-12-05T18:07:34Z

Ivierno3: /* External links */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation also be be emitted sinusoidally?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 
<math>v_y=\frac{dy}{dt}=wymax\cos(wt)</math> <math>a_y=\frac{dv_y}{dt}=-w^2ymax\sin(wt)</math>

===Amplitude===
[[File:Amp.gif|left|500px|thumb|Finding amplitude]]
Amplitude is the height of the maximum peak during oscillation. As seen from the diagram, we only measure the distance from the x axis and do not include the area below the axis. The amplitude is also the maximum magnitude of the electric field.

===Period===
[[File:Period.jpg|thumb|200px|Finding period]]
The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle. As seen in the diagram, one cycle begins at 1 second and ends at 5 seconds. Thus the period of this graph would be four seconds.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by <math>f=\frac{w}{2pi}=\frac{1}{T}</math>.

===Wavelength===
[[File:Wavelength .jpg]]
 Wavelength is used to describe sinusoidal electromagnetic radiation. The wavelength is the distance between the 2 maximum points and thus is calculated by using speed of light and frequency. wavelength<math>=cT</math> and <math>T=\frac{1}{f}</math>
 Electromagnetic radiation of different wavelengths have different names such as x-ray or microwaves. Radiation with certain wavelengths also possess certain qualities such as wavelengths of 400nm to 700nm are known as visible light as they can be seen by the human eye.

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is
#Another way is using the it of the arrival of the radiative electric field.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space through which light wave has to travel to water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength.

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Show that the electromagnetic radiation emitted is sinusoidally when the charge is moving sinusoidally.

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

http://physics.tutorvista.com/waves/wave-frequency.html
http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-3-Biology-Vol-1/Electromagnetic-Spectrum-Real-life-applications.html
http://www.pstcc.edu/departments/natural_behavioral_sciences/Web%20Physics/Chapter016.htm

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Sinusoidal Electromagnetic Radiaton

2015-12-05T18:06:48Z

Ivierno3: /* External links */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation also be be emitted sinusoidally?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 
<math>v_y=\frac{dy}{dt}=wymax\cos(wt)</math> <math>a_y=\frac{dv_y}{dt}=-w^2ymax\sin(wt)</math>

===Amplitude===
[[File:Amp.gif|left|500px|thumb|Finding amplitude]]
Amplitude is the height of the maximum peak during oscillation. As seen from the diagram, we only measure the distance from the x axis and do not include the area below the axis. The amplitude is also the maximum magnitude of the electric field.

===Period===
[[File:Period.jpg|thumb|200px|Finding period]]
The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle. As seen in the diagram, one cycle begins at 1 second and ends at 5 seconds. Thus the period of this graph would be four seconds.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by <math>f=\frac{w}{2pi}=\frac{1}{T}</math>.

===Wavelength===
[[File:Wavelength .jpg]]
 Wavelength is used to describe sinusoidal electromagnetic radiation. The wavelength is the distance between the 2 maximum points and thus is calculated by using speed of light and frequency. wavelength<math>=cT</math> and <math>T=\frac{1}{f}</math>
 Electromagnetic radiation of different wavelengths have different names such as x-ray or microwaves. Radiation with certain wavelengths also possess certain qualities such as wavelengths of 400nm to 700nm are known as visible light as they can be seen by the human eye.

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is
#Another way is using the it of the arrival of the radiative electric field.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space through which light wave has to travel to water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength.

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Show that the electromagnetic radiation emitted is sinusoidally when the charge is moving sinusoidally.

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
http://www.tapir.caltech.edu/~teviet/Waves/empulse.html https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&ved=0ahUKEwiryKbZ48HJAhXEQyYKHfKpArQQjRwIBw&url=http%3A%2F%2Fwww.edn.com%2FHome%2FPrintView%3FcontentItemId%3D4018934&psig=AFQjCNFhkmO6iOffgv1gXiFATzPxD151Xw&ust=1449303838812175
http://physics.tutorvista.com/waves/wave-frequency.html
http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-3-Biology-Vol-1/Electromagnetic-Spectrum-Real-life-applications.html
http://www.pstcc.edu/departments/natural_behavioral_sciences/Web%20Physics/Chapter016.htm

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Sinusoidal Electromagnetic Radiaton

2015-12-04T18:38:39Z

Ivierno3: /* Wavelength */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation also be be emitted sinusoidally?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 
<math>v_y=\frac{dy}{dt}=wymax\cos(wt)</math> <math>a_y=\frac{dv_y}{dt}=-w^2ymax\sin(wt)</math>

===Amplitude===
[[File:Amp.gif|left|500px|thumb|Finding amplitude]]
Amplitude is the height of the maximum peak during oscillation. As seen from the diagram, we only measure the distance from the x axis and do not include the area below the axis. The amplitude is also the maximum magnitude of the electric field.

===Period===
[[File:Period.jpg|thumb|200px|Finding period]]
The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle. As seen in the diagram, one cycle begins at 1 second and ends at 5 seconds. Thus the period of this graph would be four seconds.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by <math>f=\frac{w}{2pi}=\frac{1}{T}</math>.

===Wavelength===
[[File:Wavelength .jpg]]
 Wavelength is used to describe sinusoidal electromagnetic radiation. The wavelength is the distance between the 2 maximum points and thus is calculated by using speed of light and frequency. wavelength<math>=cT</math> and <math>T=\frac{1}{f}</math>
 Electromagnetic radiation of different wavelengths have different names such as x-ray or microwaves. Radiation with certain wavelengths also possess certain qualities such as wavelengths of 400nm to 700nm are known as visible light as they can be seen by the human eye.

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is
#Another way is using the it of the arrival of the radiative electric field.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space through which light wave has to travel to water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength.

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Show that the electromagnetic radiation emitted is sinusoidally when the charge is moving sinusoidally.

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Sinusoidal Electromagnetic Radiaton

2015-12-04T18:37:44Z

Ivierno3: /* Wavelength */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation also be be emitted sinusoidally?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 
<math>v_y=\frac{dy}{dt}=wymax\cos(wt)</math> <math>a_y=\frac{dv_y}{dt}=-w^2ymax\sin(wt)</math>

===Amplitude===
[[File:Amp.gif|left|500px|thumb|Finding amplitude]]
Amplitude is the height of the maximum peak during oscillation. As seen from the diagram, we only measure the distance from the x axis and do not include the area below the axis. The amplitude is also the maximum magnitude of the electric field.

===Period===
[[File:Period.jpg|thumb|200px|Finding period]]
The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle. As seen in the diagram, one cycle begins at 1 second and ends at 5 seconds. Thus the period of this graph would be four seconds.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by <math>f=\frac{w}{2pi}=\frac{1}{T}</math>.

===Wavelength===
[[File:Wavelength .jpg]]
 Wavelength is used to describe sinusoidal electromagnetic radiation. The wavelength is the distance between the 2 maximum points and thus is calculated by using speed of light and frequency. wavelength<math>=cT</math> and <math>T=\frac{1}{f}</math>
 Electromagnetic radiation of different wavelengths have different names such as x-ray or microwaves. Radiation with certain wavelengths also possess certain qualities such as al wavelengths of 400nm to 700nm are known as visible light as they can be seen by the human eye.

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is
#Another way is using the it of the arrival of the radiative electric field.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space through which light wave has to travel to water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength.

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Show that the electromagnetic radiation emitted is sinusoidally when the charge is moving sinusoidally.

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Sinusoidal Electromagnetic Radiaton

2015-12-04T18:36:24Z

Ivierno3: /* Wavelength */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation also be be emitted sinusoidally?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 
<math>v_y=\frac{dy}{dt}=wymax\cos(wt)</math> <math>a_y=\frac{dv_y}{dt}=-w^2ymax\sin(wt)</math>

===Amplitude===
[[File:Amp.gif|left|500px|thumb|Finding amplitude]]
Amplitude is the height of the maximum peak during oscillation. As seen from the diagram, we only measure the distance from the x axis and do not include the area below the axis. The amplitude is also the maximum magnitude of the electric field.

===Period===
[[File:Period.jpg|thumb|200px|Finding period]]
The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle. As seen in the diagram, one cycle begins at 1 second and ends at 5 seconds. Thus the period of this graph would be four seconds.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by <math>f=\frac{w}{2pi}=\frac{1}{T}</math>.

===Wavelength===
[[File:Wavelength .jpg]]
Wavelength is used to describe sinusoidal electromagnetic radiation. The wavelength is the distance between the 2 maximum points and thus is calculated by using speed of light and frequency. wavelength<math>=cT</math> and <math>T=\frac{1}{f}</math>
 Electromagnetic radiation of different wavelengths have different names such as x-ray or microwaves. Radiation with certain wavelengths also possess certain qualities such as al wavelengths of 400nm to 700nm are known as visible light as they can be seen by the human eye.

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is
#Another way is using the it of the arrival of the radiative electric field.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space through which light wave has to travel to water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength.

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Show that the electromagnetic radiation emitted is sinusoidally when the charge is moving sinusoidally.

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Sinusoidal Electromagnetic Radiaton

2015-12-04T18:35:38Z

Ivierno3: /* Wavelength */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation also be be emitted sinusoidally?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 
<math>v_y=\frac{dy}{dt}=wymax\cos(wt)</math> <math>a_y=\frac{dv_y}{dt}=-w^2ymax\sin(wt)</math>

===Amplitude===
[[File:Amp.gif|left|500px|thumb|Finding amplitude]]
Amplitude is the height of the maximum peak during oscillation. As seen from the diagram, we only measure the distance from the x axis and do not include the area below the axis. The amplitude is also the maximum magnitude of the electric field.

===Period===
[[File:Period.jpg|thumb|200px|Finding period]]
The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle. As seen in the diagram, one cycle begins at 1 second and ends at 5 seconds. Thus the period of this graph would be four seconds.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by <math>f=\frac{w}{2pi}=\frac{1}{T}</math>.

===Wavelength===
[[File:Wavelength .jpg]]
Wavelength is used to describe sinusoidal electromagnetic radiation. The wavelength is the distance between the 2 maximum points and thus is calculated by using speed of light and frequency. wavelength<math>=cT</math> and <math>T=\frac{1}{f}</math>
Electromagnetic radiation of different wavelengths have different names such as x-ray or microwaves. Radiation with certain wavelengths also possess certain qualities such as al wavelengths of 400nm to 700nm are known as visible light as they can be seen by the human eye.

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is
#Another way is using the it of the arrival of the radiative electric field.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space through which light wave has to travel to water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength.

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Show that the electromagnetic radiation emitted is sinusoidally when the charge is moving sinusoidally.

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Sinusoidal Electromagnetic Radiaton

2015-12-04T18:35:16Z

Ivierno3: /* Wavelength */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation also be be emitted sinusoidally?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 
<math>v_y=\frac{dy}{dt}=wymax\cos(wt)</math> <math>a_y=\frac{dv_y}{dt}=-w^2ymax\sin(wt)</math>

===Amplitude===
[[File:Amp.gif|left|500px|thumb|Finding amplitude]]
Amplitude is the height of the maximum peak during oscillation. As seen from the diagram, we only measure the distance from the x axis and do not include the area below the axis. The amplitude is also the maximum magnitude of the electric field.

===Period===
[[File:Period.jpg|thumb|200px|Finding period]]
The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle. As seen in the diagram, one cycle begins at 1 second and ends at 5 seconds. Thus the period of this graph would be four seconds.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by <math>f=\frac{w}{2pi}=\frac{1}{T}</math>.

===Wavelength===
[[File:Wavelength .jpg]]
Wavelength is used to describe sinusoidal electromagnetic radiation. The wavelength is the distance between the 2 maximum points and thus is calculated by using speed of light and frequency. wavelength<math>=cT</math> and <math>T={1}{f}</math>
Electromagnetic radiation of different wavelengths have different names such as x-ray or microwaves. Radiation with certain wavelengths also possess certain qualities such as al wavelengths of 400nm to 700nm are known as visible light as they can be seen by the human eye.

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is
#Another way is using the it of the arrival of the radiative electric field.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space through which light wave has to travel to water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength.

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Show that the electromagnetic radiation emitted is sinusoidally when the charge is moving sinusoidally.

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Sinusoidal Electromagnetic Radiaton

2015-12-04T18:33:07Z

Ivierno3: /* Wavelength */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation also be be emitted sinusoidally?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 
<math>v_y=\frac{dy}{dt}=wymax\cos(wt)</math> <math>a_y=\frac{dv_y}{dt}=-w^2ymax\sin(wt)</math>

===Amplitude===
[[File:Amp.gif|left|500px|thumb|Finding amplitude]]
Amplitude is the height of the maximum peak during oscillation. As seen from the diagram, we only measure the distance from the x axis and do not include the area below the axis. The amplitude is also the maximum magnitude of the electric field.

===Period===
[[File:Period.jpg|thumb|200px|Finding period]]
The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle. As seen in the diagram, one cycle begins at 1 second and ends at 5 seconds. Thus the period of this graph would be four seconds.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by <math>f=\frac{w}{2pi}=\frac{1}{T}</math>.

===Wavelength===
[[File:Wavelength .jpg]]
Wavelength is used to describe sinusoidal electromagnetic radiation. The wavelength is the distance between the 2 maximum points and thus is calculated by using speed of light and frequency. wavelength<math>=cT and T={1}{f}</math>

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is
#Another way is using the it of the arrival of the radiative electric field.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space through which light wave has to travel to water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength.

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Show that the electromagnetic radiation emitted is sinusoidally when the charge is moving sinusoidally.

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

File:Wavelength .jpg

2015-12-04T18:32:54Z

Ivierno3:

Sinusoidal Electromagnetic Radiaton

2015-12-04T18:32:37Z

Ivierno3: /* Wavelength */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation also be be emitted sinusoidally?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 
<math>v_y=\frac{dy}{dt}=wymax\cos(wt)</math> <math>a_y=\frac{dv_y}{dt}=-w^2ymax\sin(wt)</math>

===Amplitude===
[[File:Amp.gif|left|500px|thumb|Finding amplitude]]
Amplitude is the height of the maximum peak during oscillation. As seen from the diagram, we only measure the distance from the x axis and do not include the area below the axis. The amplitude is also the maximum magnitude of the electric field.

===Period===
[[File:Period.jpg|thumb|200px|Finding period]]
The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle. As seen in the diagram, one cycle begins at 1 second and ends at 5 seconds. Thus the period of this graph would be four seconds.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by <math>f=\frac{w}{2pi}=\frac{1}{T}</math>.

===Wavelength===
[[File:wavelength .jpg]]
Wavelength is used to describe sinusoidal electromagnetic radiation. The wavelength is the distance between the 2 maximum points and thus is calculated by using speed of light and frequency. wavelength<math>=cT and T={1}{f}</math>

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is
#Another way is using the it of the arrival of the radiative electric field.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space through which light wave has to travel to water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength.

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Show that the electromagnetic radiation emitted is sinusoidally when the charge is moving sinusoidally.

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Sinusoidal Electromagnetic Radiaton

2015-12-04T18:25:58Z

Ivierno3: /* Frequency */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation also be be emitted sinusoidally?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 
<math>v_y=\frac{dy}{dt}=wymax\cos(wt)</math> <math>a_y=\frac{dv_y}{dt}=-w^2ymax\sin(wt)</math>

===Amplitude===
[[File:Amp.gif|left|500px|thumb|Finding amplitude]]
Amplitude is the height of the maximum peak during oscillation. As seen from the diagram, we only measure the distance from the x axis and do not include the area below the axis. The amplitude is also the maximum magnitude of the electric field.

===Period===
[[File:Period.jpg|thumb|200px|Finding period]]
The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle. As seen in the diagram, one cycle begins at 1 second and ends at 5 seconds. Thus the period of this graph would be four seconds.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by <math>f=\frac{w}{2pi}=\frac{1}{T}</math>.

===Wavelength===

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is
#Another way is using the it of the arrival of the radiative electric field.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space through which light wave has to travel to water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength.

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Show that the electromagnetic radiation emitted is sinusoidally when the charge is moving sinusoidally.

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Sinusoidal Electromagnetic Radiaton

2015-12-04T18:16:00Z

Ivierno3: /* Charge Moving Sinusoidally */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation also be be emitted sinusoidally?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 
<math>v_y=\frac{dy}{dt}=wymax\cos(wt)</math> <math>a_y=\frac{dv_y}{dt}=-w^2ymax\sin(wt)</math>

===Amplitude===
[[File:Amp.gif|left|500px|thumb|Finding amplitude]]
Amplitude is the height of the maximum peak during oscillation. As seen from the diagram, we only measure the distance from the x axis and do not include the area below the axis. The amplitude is also the maximum magnitude of the electric field.

===Period===
[[File:Period.jpg|thumb|200px|Finding period]]
The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle. As seen in the diagram, one cycle begins at 1 second and ends at 5 seconds. Thus the period of this graph would be four seconds.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by <math>f=\frac{w}{2pi}</math>.

===Wavelength===

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is
#Another way is using the it of the arrival of the radiative electric field.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space through which light wave has to travel to water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength.

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Show that the electromagnetic radiation emitted is sinusoidally when the charge is moving sinusoidally.

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Sinusoidal Electromagnetic Radiaton

2015-12-04T18:10:29Z

Ivierno3: /* Frequency */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation also be be emitted sinusoidally?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 
<math>v_y=\frac{dy}{dt}=wymax\cos(wt)</math> <math>a_y=\frac{dv_y}{dt}=-w^2ymax\sin(wt)</math>

===Amplitude===
[[File:Amp.gif|left|500px|thumb|Finding amplitude]]
Amplitude is the height of the maximum peak during oscillation. As seen from the diagram, we only measure the distance from the x axis and do not include the area below the axis. The amplitude is also the maximum magnitude of the electric field.

===Period===
[[File:Period.jpg|thumb|200px|Finding period]]
The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle. As seen in the diagram, one cycle begins at 1 second and ends at 5 seconds. Thus the period of this graph would be four seconds.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by <math>f=\frac{w}{2pi}</math>.

===Wavelength===

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is
#Another way is using the it of the arrival of the radiative electric field.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space through which light wave has to travel to water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength.

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Show that the electromagnetic radiation emitted is sinusoidally when the charge is moving sinusoidally.

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Sinusoidal Electromagnetic Radiaton

2015-12-04T18:09:14Z

Ivierno3: /* Amplitude */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation also be be emitted sinusoidally?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 
<math>v_y=\frac{dy}{dt}=wymax\cos(wt)</math> <math>a_y=\frac{dv_y}{dt}=-w^2ymax\sin(wt)</math>

===Amplitude===
[[File:Amp.gif|left|500px|thumb|Finding amplitude]]
Amplitude is the height of the maximum peak during oscillation. As seen from the diagram, we only measure the distance from the x axis and do not include the area below the axis. The amplitude is also the maximum magnitude of the electric field.

===Period===
[[File:Period.jpg|thumb|200px|Finding period]]
The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle. As seen in the diagram, one cycle begins at 1 second and ends at 5 seconds. Thus the period of this graph would be four seconds.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by f=w/2pi.

===Wavelength===

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is
#Another way is using the it of the arrival of the radiative electric field.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space through which light wave has to travel to water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength.

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Show that the electromagnetic radiation emitted is sinusoidally when the charge is moving sinusoidally.

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Sinusoidal Electromagnetic Radiaton

2015-12-04T18:08:35Z

Ivierno3: /* Amplitude */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation also be be emitted sinusoidally?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 
<math>v_y=\frac{dy}{dt}=wymax\cos(wt)</math> <math>a_y=\frac{dv_y}{dt}=-w^2ymax\sin(wt)</math>

===Amplitude===
[[File:Amp.gif|500px|thumb|Finding amplitude]]
Amplitude is the height of the maximum peak during oscillation. As seen from the diagram, we only measure the distance from the x axis and do not include the area below the axis. The amplitude is also the maximum magnitude of the electric field.

===Period===
[[File:Period.jpg|thumb|200px|Finding period]]
The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle. As seen in the diagram, one cycle begins at 1 second and ends at 5 seconds. Thus the period of this graph would be four seconds.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by f=w/2pi.

===Wavelength===

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is
#Another way is using the it of the arrival of the radiative electric field.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space through which light wave has to travel to water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength.

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Show that the electromagnetic radiation emitted is sinusoidally when the charge is moving sinusoidally.

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Sinusoidal Electromagnetic Radiaton

2015-12-04T18:08:22Z

Ivierno3: /* Period */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation also be be emitted sinusoidally?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 
<math>v_y=\frac{dy}{dt}=wymax\cos(wt)</math> <math>a_y=\frac{dv_y}{dt}=-w^2ymax\sin(wt)</math>

===Amplitude===
[[File:Amp.gif|right|500px|thumb|Finding amplitude]]
Amplitude is the height of the maximum peak during oscillation. As seen from the diagram, we only measure the distance from the x axis and do not include the area below the axis. The amplitude is also the maximum magnitude of the electric field.

===Period===
[[File:Period.jpg|thumb|200px|Finding period]]
The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle. As seen in the diagram, one cycle begins at 1 second and ends at 5 seconds. Thus the period of this graph would be four seconds.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by f=w/2pi.

===Wavelength===

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is
#Another way is using the it of the arrival of the radiative electric field.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space through which light wave has to travel to water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength.

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Show that the electromagnetic radiation emitted is sinusoidally when the charge is moving sinusoidally.

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Sinusoidal Electromagnetic Radiaton

2015-12-04T18:08:04Z

Ivierno3: /* Period */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation also be be emitted sinusoidally?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 
<math>v_y=\frac{dy}{dt}=wymax\cos(wt)</math> <math>a_y=\frac{dv_y}{dt}=-w^2ymax\sin(wt)</math>

===Amplitude===
[[File:Amp.gif|right|500px|thumb|Finding amplitude]]
Amplitude is the height of the maximum peak during oscillation. As seen from the diagram, we only measure the distance from the x axis and do not include the area below the axis. The amplitude is also the maximum magnitude of the electric field.

===Period===
[[File:Period.jpg|thumb|200px]]
The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle. As seen in the diagram, one cycle begins at 1 second and ends at 5 seconds. Thus the period of this graph would be four seconds.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by f=w/2pi.

===Wavelength===

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is
#Another way is using the it of the arrival of the radiative electric field.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space through which light wave has to travel to water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength.

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Show that the electromagnetic radiation emitted is sinusoidally when the charge is moving sinusoidally.

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Sinusoidal Electromagnetic Radiaton

2015-12-04T18:07:44Z

Ivierno3: /* Period */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation also be be emitted sinusoidally?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 
<math>v_y=\frac{dy}{dt}=wymax\cos(wt)</math> <math>a_y=\frac{dv_y}{dt}=-w^2ymax\sin(wt)</math>

===Amplitude===
[[File:Amp.gif|right|500px|thumb|Finding amplitude]]
Amplitude is the height of the maximum peak during oscillation. As seen from the diagram, we only measure the distance from the x axis and do not include the area below the axis. The amplitude is also the maximum magnitude of the electric field.

===Period===
[[File:Period.jpg]]
The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle. As seen in the diagram, one cycle begins at 1 second and ends at 5 seconds. Thus the period of this graph would be four seconds.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by f=w/2pi.

===Wavelength===

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is
#Another way is using the it of the arrival of the radiative electric field.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space through which light wave has to travel to water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength.

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Show that the electromagnetic radiation emitted is sinusoidally when the charge is moving sinusoidally.

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

File:Period.jpg

2015-12-04T18:07:05Z

Ivierno3:

Sinusoidal Electromagnetic Radiaton

2015-12-04T18:06:49Z

Ivierno3: /* Period */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation also be be emitted sinusoidally?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 
<math>v_y=\frac{dy}{dt}=wymax\cos(wt)</math> <math>a_y=\frac{dv_y}{dt}=-w^2ymax\sin(wt)</math>

===Amplitude===
[[File:Amp.gif|right|500px|thumb|Finding amplitude]]
Amplitude is the height of the maximum peak during oscillation. As seen from the diagram, we only measure the distance from the x axis and do not include the area below the axis. The amplitude is also the maximum magnitude of the electric field.

===Period===
[[File:period.jpg]]
The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle. As seen in the diagram, one cycle begins at 1 second and ends at 5 seconds. Thus the period of this graph would be four seconds.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by f=w/2pi.

===Wavelength===

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is
#Another way is using the it of the arrival of the radiative electric field.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space through which light wave has to travel to water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength.

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Show that the electromagnetic radiation emitted is sinusoidally when the charge is moving sinusoidally.

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Sinusoidal Electromagnetic Radiaton

2015-12-04T18:03:35Z

Ivierno3: /* Amplitude */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation also be be emitted sinusoidally?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 
<math>v_y=\frac{dy}{dt}=wymax\cos(wt)</math> <math>a_y=\frac{dv_y}{dt}=-w^2ymax\sin(wt)</math>

===Amplitude===
[[File:Amp.gif|right|500px|thumb|Finding amplitude]]
Amplitude is the height of the maximum peak during oscillation. As seen from the diagram, we only measure the distance from the x axis and do not include the area below the axis. The amplitude is also the maximum magnitude of the electric field.

===Period===

The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by f=w/2pi.

===Wavelength===

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is
#Another way is using the it of the arrival of the radiative electric field.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space through which light wave has to travel to water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength.

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Show that the electromagnetic radiation emitted is sinusoidally when the charge is moving sinusoidally.

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Sinusoidal Electromagnetic Radiaton

2015-12-04T18:03:25Z

Ivierno3: /* Amplitude */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation also be be emitted sinusoidally?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 
<math>v_y=\frac{dy}{dt}=wymax\cos(wt)</math> <math>a_y=\frac{dv_y}{dt}=-w^2ymax\sin(wt)</math>

===Amplitude===
[[File:Amp.gif|right|300px|thumb|Finding amplitude]]
Amplitude is the height of the maximum peak during oscillation. As seen from the diagram, we only measure the distance from the x axis and do not include the area below the axis. The amplitude is also the maximum magnitude of the electric field.

===Period===

The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by f=w/2pi.

===Wavelength===

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is
#Another way is using the it of the arrival of the radiative electric field.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space through which light wave has to travel to water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength.

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Show that the electromagnetic radiation emitted is sinusoidally when the charge is moving sinusoidally.

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Sinusoidal Electromagnetic Radiaton

2015-12-04T18:03:16Z

Ivierno3: /* Amplitude */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation also be be emitted sinusoidally?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 
<math>v_y=\frac{dy}{dt}=wymax\cos(wt)</math> <math>a_y=\frac{dv_y}{dt}=-w^2ymax\sin(wt)</math>

===Amplitude===
[[File:Amp.gif|right|200px|thumb|Finding amplitude]]
Amplitude is the height of the maximum peak during oscillation. As seen from the diagram, we only measure the distance from the x axis and do not include the area below the axis. The amplitude is also the maximum magnitude of the electric field.

===Period===

The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by f=w/2pi.

===Wavelength===

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is
#Another way is using the it of the arrival of the radiative electric field.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space through which light wave has to travel to water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength.

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Show that the electromagnetic radiation emitted is sinusoidally when the charge is moving sinusoidally.

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Sinusoidal Electromagnetic Radiaton

2015-12-04T18:02:54Z

Ivierno3: /* Amplitude */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation also be be emitted sinusoidally?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 
<math>v_y=\frac{dy}{dt}=wymax\cos(wt)</math> <math>a_y=\frac{dv_y}{dt}=-w^2ymax\sin(wt)</math>

===Amplitude===
[[File:Amp.gif|right|thumb|Finding amplitude]]
Amplitude is the height of the maximum peak during oscillation. As seen from the diagram, we only measure the distance from the x axis and do not include the area below the axis. The amplitude is also the maximum magnitude of the electric field.

===Period===

The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by f=w/2pi.

===Wavelength===

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is
#Another way is using the it of the arrival of the radiative electric field.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space through which light wave has to travel to water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength.

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Show that the electromagnetic radiation emitted is sinusoidally when the charge is moving sinusoidally.

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Sinusoidal Electromagnetic Radiaton

2015-12-04T18:02:26Z

Ivierno3: /* Amplitude */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation also be be emitted sinusoidally?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 
<math>v_y=\frac{dy}{dt}=wymax\cos(wt)</math> <math>a_y=\frac{dv_y}{dt}=-w^2ymax\sin(wt)</math>

===Amplitude===
[[File:Amp.gif]]
Amplitude is the height of the maximum peak during oscillation. As seen from the diagram, we only measure the distance from the x axis and do not include the area below the axis. The amplitude is also the maximum magnitude of the electric field.

===Period===

The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by f=w/2pi.

===Wavelength===

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is
#Another way is using the it of the arrival of the radiative electric field.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space through which light wave has to travel to water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength.

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Show that the electromagnetic radiation emitted is sinusoidally when the charge is moving sinusoidally.

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Sinusoidal Electromagnetic Radiaton

2015-12-04T18:01:14Z

Ivierno3: /* Amplitude */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation also be be emitted sinusoidally?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 
<math>v_y=\frac{dy}{dt}=wymax\cos(wt)</math> <math>a_y=\frac{dv_y}{dt}=-w^2ymax\sin(wt)</math>

===Amplitude===
[[File:Amp.gif|thumb|Finding Amplitude]]
Amplitude is the height of the maximum peak during oscillation. As seen from the diagram, we only measure the distance from the x axis and do not include the area below the axis. The amplitude is also the maximum magnitude of the electric field.

===Period===

The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by f=w/2pi.

===Wavelength===

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is
#Another way is using the it of the arrival of the radiative electric field.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space through which light wave has to travel to water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength.

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Show that the electromagnetic radiation emitted is sinusoidally when the charge is moving sinusoidally.

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Sinusoidal Electromagnetic Radiaton

2015-12-04T18:00:49Z

Ivierno3: /* Amplitude */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation also be be emitted sinusoidally?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 
<math>v_y=\frac{dy}{dt}=wymax\cos(wt)</math> <math>a_y=\frac{dv_y}{dt}=-w^2ymax\sin(wt)</math>

===Amplitude===
[[File:amp.gif|thumb|Finding Amplitude]]
Amplitude is the height of the maximum peak during oscillation. As seen from the diagram, we only measure the distance from the x axis and do not include the area below the axis. The amplitude is also the maximum magnitude of the electric field.

===Period===

The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by f=w/2pi.

===Wavelength===

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is
#Another way is using the it of the arrival of the radiative electric field.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space through which light wave has to travel to water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength.

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Show that the electromagnetic radiation emitted is sinusoidally when the charge is moving sinusoidally.

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Sinusoidal Electromagnetic Radiaton

2015-12-04T18:00:26Z

Ivierno3: /* Amplitude */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation also be be emitted sinusoidally?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 
<math>v_y=\frac{dy}{dt}=wymax\cos(wt)</math> <math>a_y=\frac{dv_y}{dt}=-w^2ymax\sin(wt)</math>

===Amplitude===
[[File:amp.gif|thumb|Finding Amplitude]]
Amplitude is the height of the maximum peak during oscillation. As seen from the diagram, we only measure the distance from the x axis and do not include the area below the axis. The amplitude is also the maximum magnitude of the electric field. [[File:amp.gif|thumb|Finding Amplitude]]

===Period===

The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by f=w/2pi.

===Wavelength===

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is
#Another way is using the it of the arrival of the radiative electric field.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space through which light wave has to travel to water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength.

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Show that the electromagnetic radiation emitted is sinusoidally when the charge is moving sinusoidally.

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

File:Amp.gif

2015-12-04T18:00:08Z

Ivierno3:

Sinusoidal Electromagnetic Radiaton

2015-12-04T17:59:41Z

Ivierno3: /* Amplitude */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation also be be emitted sinusoidally?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 
<math>v_y=\frac{dy}{dt}=wymax\cos(wt)</math> <math>a_y=\frac{dv_y}{dt}=-w^2ymax\sin(wt)</math>

===Amplitude===

Amplitude is the height of the maximum peak during oscillation. As seen from the diagram, we only measure the distance from the x axis and do not include the area below the axis. The amplitude is also the maximum magnitude of the electric field. [[File:amp.gif|thumb|Finding Amplitude]]

===Period===

The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by f=w/2pi.

===Wavelength===

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is
#Another way is using the it of the arrival of the radiative electric field.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space through which light wave has to travel to water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength.

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Show that the electromagnetic radiation emitted is sinusoidally when the charge is moving sinusoidally.

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Sinusoidal Electromagnetic Radiaton

2015-12-04T17:55:06Z

Ivierno3: /* Amplitude */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation also be be emitted sinusoidally?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 
<math>v_y=\frac{dy}{dt}=wymax\cos(wt)</math> <math>a_y=\frac{dv_y}{dt}=-w^2ymax\sin(wt)</math>

===Amplitude===

Height of the peak of wave perpendicular to x axis. The amplitude is also the maximum magnitude of the electric field.

===Period===

The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by f=w/2pi.

===Wavelength===

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is
#Another way is using the it of the arrival of the radiative electric field.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space through which light wave has to travel to water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength.

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Show that the electromagnetic radiation emitted is sinusoidally when the charge is moving sinusoidally.

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Sinusoidal Electromagnetic Radiaton

2015-12-04T17:54:36Z

Ivierno3: /* Charge Moving Sinusoidally */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation also be be emitted sinusoidally?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 
<math>v_y=\frac{dy}{dt}=wymax\cos(wt)</math> <math>a_y=\frac{dv_y}{dt}=-w^2ymax\sin(wt)</math>

===Amplitude===

Amplitude: Height of the peak of wave perpendicular to x axis. The amplitude is also the maximum magnitude of the electric field.

===Period===

The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by f=w/2pi.

===Wavelength===

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is
#Another way is using the it of the arrival of the radiative electric field.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space through which light wave has to travel to water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength.

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Show that the electromagnetic radiation emitted is sinusoidally when the charge is moving sinusoidally.

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Sinusoidal Electromagnetic Radiaton

2015-12-04T17:53:56Z

Ivierno3: /* Charge Moving Sinusoidally */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation also be be emitted sinusoidally?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 
<math>v_y=\frac{dy}{dt}=wymax\cos(wt) a_y=\frac{dv_y}{dt}=-w^2ymax\sin(wt)</math>

===Amplitude===

Amplitude: Height of the peak of wave perpendicular to x axis. The amplitude is also the maximum magnitude of the electric field.

===Period===

The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by f=w/2pi.

===Wavelength===

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is
#Another way is using the it of the arrival of the radiative electric field.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space through which light wave has to travel to water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength.

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Show that the electromagnetic radiation emitted is sinusoidally when the charge is moving sinusoidally.

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Sinusoidal Electromagnetic Radiaton

2015-12-04T17:52:09Z

Ivierno3: /* Charge Moving Sinusoidally */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation also be be emitted sinusoidally?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 
<math>v_y=frac{dy}{dt}=w\ymax\cos(wt) a_y=frac{dv_y}{dt}=-w^2ymax\sin(wt)</math>

===Amplitude===

Amplitude: Height of the peak of wave perpendicular to x axis. The amplitude is also the maximum magnitude of the electric field.

===Period===

The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by f=w/2pi.

===Wavelength===

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is
#Another way is using the it of the arrival of the radiative electric field.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space through which light wave has to travel to water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength.

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Show that the electromagnetic radiation emitted is sinusoidally when the charge is moving sinusoidally.

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Sinusoidal Electromagnetic Radiaton

2015-12-04T17:48:01Z

Ivierno3: /* Charge Moving Sinusoidally */

Made and claimed by Ida De Vierno

==The Main Idea==

Being able to mathematically relate the speed, wavelength and period of a sinusoidal electromagnetic wave. Understanding how radiation emitted is affected by a charge moving sinusoidally.

===Electromagnetic Radiation===
When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of a stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.[[File:wiki2.gif]]

===Charge Moving Sinusoidally===
[[File:Circularcharge.jpg|right|thumb|Circular]][[File:wiki4.png|200px|right|thumb|Sinusoidal Waves]]Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

 When a charge is moved sinusoidally, we can find the position of charge by
 <math>y=ymax\sin(wt)</math> where <math>w</math> is the angular frequency in radians per second.

 Will the electromagnetic radiation also be be emitted sinusoidally?
Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. (Steps can be found in examples) This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation. 

===Amplitude===

Amplitude: Height of the peak of wave perpendicular to x axis. The amplitude is also the maximum magnitude of the electric field.

===Period===

The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle.

===Frequency===

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse or Hertz. Frequency is also related to angular frequent w in radians per second by f=w/2pi.

===Wavelength===

===Speed===

Speed of propagation of electromagnetic wave can be measured in two different ways.
#The first way is by following the maximum amplitude (the peak of the oscillation). You will notice that it travels one wavelength in a period. Thus speed of crest is
#Another way is using the it of the arrival of the radiative electric field.

These two ways of calculating speed will give you a constant answer in a vacuum. However discrepancies can occur in space through which light wave has to travel to water, glass or even air.

===Polarized Radiation===

Polarization refers to the orientation of electric field, in which it can be aligned only along one axis.
Radiation can also be unpolarized as in the case of natural light due to the charges oscillating along different directions.

===Electromagnetic Spectrum===

Electromagnetic spectrum is the range of all types of electromagnetic radiation, according to frequency and wavelength.

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Show that the electromagnetic radiation emitted is sinusoidally when the charge is moving sinusoidally.

==Connectedness==

Is there an interesting industrial application?
Understanding electromagnetic radiation and being able to calculate wavelength and frequency is needed in the areas of communication such as the television and the radio. Knowing the fundamentals has resulted in the development of technology for sending speech and music through the airwaves.

==History==

Electromagnetic waves was first discovered in the nineteenth century when an unexpected correlation between electric phenomena and velocity of light was found. James Maxwell who founded the Maxwell equation not only realized that electric field and magnetic field cover together form electromagnetic wave but that changing magnetic field will cause a change in electric field. In 1887, using Maxwell's theories, Heinrich Hertz produced waves and also found methods to detect these ways. Using two rods to serve as receivers and a spark gap to act as the antennae. Every time a wave was picked up, it would create a spark. By doing this, Hertz proved that signals had the properties of electromagnetic waves. The unit for frequency was thus named after him.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]