Physics Book - User contributions [en]

Electromagnetic Propagation

2015-12-03T02:23:45Z

ChiChiO:

Electromagnetic Propagation Model
BY CHIAGOZIEM OBI

==The Main Idea==

What is the ideal model for the propagation of electromagnetic waves? Does it look like a sheet of electrons? Maybe it can be described as a spring? A mountain? No! The following explains why the best model is a traveling slab of perpendicular waves that oscillate back and forth.

==A Mathematical Model: Maxwell's Equations==

===Gauss's Law for Electricity and Magnetism===
<math>\sum \phi_{electric} = \frac{q_{inside}}{\epsilon_0} = \int \vec{E} \bullet d\vec{A} </math>
<math>\sum \phi_{magnetic} = 0 = \int \vec{B} \bullet d\vec{A} </math>

===Faraday's Law===
<math> \int \vec{E} \bullet d\vec{l} = -\frac{d\phi_{magnetic}}{dt}</math>

===Ampere-Maxwell Law===
<math> \int \vec{B} \bullet d\vec{l} = \mu_0\epsilon_0\frac{d\phi_{electric}}{dt} + \mu_0I_{enclosed}</math>

==An Interactive Computational Model==

Follow this link to find an interesting little animation.

http://www.walter-fendt.de/ph14e/emwave.htm

==Proposed Model==

Waves may be a familiar concept. We can imagine waves as the familiar up-and-down movement of crests and troughs. The concept of a wave is also applicable to the physics of radiation. According to Maxwell’s equations, a time varying electric field produces a magnetic field, just as a time varying electric field produces a magnetic field. We can try to picture what such a time varying field would “look” like. Let’s propose a model for it.

We can call this single traveling box of field a pulse. There are no charges inside or outside of it. It is simply a traveling box of electric field. It generates a perpendicular magnetic field. Both electric field and magnetic field are perpendicular to the direction that the fields are moving. We can call this a “pulse” of electromagnetic field.

In order to be an acceptable model, it must satisfy all four of the equations of Maxwell. Applying Guass’s law for electricity and magnetism we see that the model works out.

===Does the Model Fit the Math?===

===Gauss's Law===
Lets use the slab as a Gauss surface. Calculate the flux through the surface. Applying Gauss' Law shows us that since there is equal amounts of magnetic and electric flux going into and out of the slab, there is no net charge or magnetic monopole through the slab.
[[File:Gauss Electric.JPG]]
[[File:Gauss_Magnetic.JPG]]

===Faraday's Law===
Applying Faraday’s law involves realizing that the pulse in moving through space, and, for an imaginary path, the flux is changing through that path. We can pick a path h high and w wide, and allow part of the path to be inside the box of pulse and some of the path to be outside the pulse, initially. A short time, Δt, later the pulse has moved, encompassing more of the path. The change in the flux is the magnitude of the magnetic field times the velocity of the particle times the height of the path.
The change in flux is equal to the emf around the path. The electric field times the height is equal to the emf. So Eh = Bvh. Simplifying that solution yields that the electric field is equal to the velocity times the magnetic field.

===Ampere-Maxwell Law===

[[File:Amperepath.JPG ]]
This law states that the magnetic field times the path length is equal to <math>\mu_0 \sum I_{enclosed}+ \frac{d\phi_{electric}}{dt}\mu_0\epsilon_0</math> The change in electric flux is equal to Evh. The magnetic field integral is Bh. Equating the two yields that <math>\mu_0\epsilon_0Evh = Bh </math> Simplifying yields that <math> B = \mu_0\epsilon_0vE</math>
So using our model of a box-like particle and applying Ampere-Maxwell’s equations to it, we’ve found that <math> E = vB </math> and <math> B = \mu_0\epsilon_0vE </math> Also the electric flux and magnetic flux equal zero. Solving for v we find that v = 3e8 m/s. This is the speed of light.

==Connectedness==
This model of electromagnetic waves allows us to predict the effects of light and other waves on matter. We know that light can be polarized into one direction, which is practical for use in optics. We also can determine the interaction between these waves and charged particles. For instance, one important idea is that electromagnetic waves carry energy. Chemists use the properties of light energy in techniques called spectroscopy. Magnetic and electric waves and fields are critical in determining structure of unknown molecules.

===History of Application===

One historical application is Nuclear magnetic resonance (NMR) imaging of chemical substances to determine structure. A sample is exposed to powerful magnetic fields, in order to align the particles. Magnetic spins of the electrons of the Hydrogen atoms. They align in the most favorable (lowest energy) alignment. Then the sample is blasting with varying frequencies of electric field (up to 300million Hz) and the frequency at which the electrons move out of alignment is recorded. This information is then used to determine structures of molecules. (Can you tell that I'm a biochem major?)

The application of this method stems from the understanding of how these waves interact with the charged particles of matter. Our models for atoms and electromagnetic waves allow us to make useful and accurate predictions about chemical structure. It is also a great tool for stressing out aspiring biochem majors. (Reading NMR graphs is very difficult. Google it. You'll see what I mean.)

== See also ==

[http://www.physicsbook.gatech.edu/Light_Scaterring:_Why_is_the_Sky_Blue Why is the Sky Blue]

===Further reading===

Matter and Interactions Textbook (Section 23.2)

===External links===
[https://www.youtube.com/watch?v=4CtnUETLIFs Quick Animation]

[https://www.youtube.com/watch?v=d50avTf0OLw Tutor Literally Yelling Information at You (JK his voice is just loud)]

[http://imagine.gsfc.nasa.gov/science/toolbox/emspectrum1.html NASA on Electromagnetic Waves]

==References==

Matter and Interactions Textbook Section 23.2

[[Category:Radiation]]

Edited by Chiagoziem Obi

Electromagnetic Propagation

2015-12-03T02:22:04Z

ChiChiO: /* Gauss's Law */

Electromagnetic Propagation Model
*BY CHIAGOZIEM OBI*

==The Main Idea==

What is the ideal model for the propagation of electromagnetic waves? Does it look like a sheet of electrons? Maybe it can be described as a spring? A mountain? No! The following explains why the best model is a traveling slab of perpendicular waves that oscillate back and forth.

==A Mathematical Model: Maxwell's Equations==

===Gauss's Law for Electricity and Magnetism===
<math>\sum \phi_{electric} = \frac{q_{inside}}{\epsilon_0} = \int \vec{E} \bullet d\vec{A} </math>
<math>\sum \phi_{magnetic} = 0 = \int \vec{B} \bullet d\vec{A} </math>

===Faraday's Law===
<math> \int \vec{E} \bullet d\vec{l} = -\frac{d\phi_{magnetic}}{dt}</math>

===Ampere-Maxwell Law===
<math> \int \vec{B} \bullet d\vec{l} = \mu_0\epsilon_0\frac{d\phi_{electric}}{dt} + \mu_0I_{enclosed}</math>

==An Interactive Computational Model==

Follow this link to find an interesting little animation.

http://www.walter-fendt.de/ph14e/emwave.htm

==Proposed Model==

Waves may be a familiar concept. We can imagine waves as the familiar up-and-down movement of crests and troughs. The concept of a wave is also applicable to the physics of radiation. According to Maxwell’s equations, a time varying electric field produces a magnetic field, just as a time varying electric field produces a magnetic field. We can try to picture what such a time varying field would “look” like. Let’s propose a model for it.

We can call this single traveling box of field a pulse. There are no charges inside or outside of it. It is simply a traveling box of electric field. It generates a perpendicular magnetic field. Both electric field and magnetic field are perpendicular to the direction that the fields are moving. We can call this a “pulse” of electromagnetic field.

In order to be an acceptable model, it must satisfy all four of the equations of Maxwell. Applying Guass’s law for electricity and magnetism we see that the model works out.

===Does the Model Fit the Math?===

===Gauss's Law===
Lets use the slab as a Gauss surface. Calculate the flux through the surface. Applying Gauss' Law shows us that since there is equal amounts of magnetic and electric flux going into and out of the slab, there is no net charge or magnetic monopole through the slab.
[[File:Gauss Electric.JPG]]
[[File:Gauss_Magnetic.JPG]]

===Faraday's Law===
Applying Faraday’s law involves realizing that the pulse in moving through space, and, for an imaginary path, the flux is changing through that path. We can pick a path h high and w wide, and allow part of the path to be inside the box of pulse and some of the path to be outside the pulse, initially. A short time, Δt, later the pulse has moved, encompassing more of the path. The change in the flux is the magnitude of the magnetic field times the velocity of the particle times the height of the path.
The change in flux is equal to the emf around the path. The electric field times the height is equal to the emf. So Eh = Bvh. Simplifying that solution yields that the electric field is equal to the velocity times the magnetic field.

===Ampere-Maxwell Law===

This law states that the magnetic field times the path length is equal to <math>\mu_0 \sum I_{enclosed}+ \frac{d\phi_{electric}}{dt}\mu_0\epsilon_0</math> The change in electric flux is equal to Evh. The magnetic field integral is Bh. Equating the two yields that <math>\mu_0\epsilon_0Evh = Bh </math> Simplifying yields that <math> B = \mu_0\epsilon_0vE</math>
So using our model of a box-like particle and applying Ampere-Maxwell’s equations to it, we’ve found that <math> E = vB </math> and <math> B = \mu_0\epsilon_0vE </math> Also the electric flux and magnetic flux equal zero. Solving for v we find that v = 3e8 m/s. This is the speed of light.

==Connectedness==
This model of electromagnetic waves allows us to predict the effects of light and other waves on matter. We know that light can be polarized into one direction, which is practical for use in optics. We also can determine the interaction between these waves and charged particles. For instance, one important idea is that electromagnetic waves carry energy. Chemists use the properties of light energy in techniques called spectroscopy. Magnetic and electric waves and fields are critical in determining structure of unknown molecules.

===History of Application===

One historical application is Nuclear magnetic resonance (NMR) imaging of chemical substances to determine structure. A sample is exposed to powerful magnetic fields, in order to align the particles. Magnetic spins of the electrons of the Hydrogen atoms. They align in the most favorable (lowest energy) alignment. Then the sample is blasting with varying frequencies of electric field (up to 300million Hz) and the frequency at which the electrons move out of alignment is recorded. This information is then used to determine structures of molecules. (Can you tell that I'm a biochem major?)

The application of this method stems from the understanding of how these waves interact with the charged particles of matter. Our models for atoms and electromagnetic waves allow us to make useful and accurate predictions about chemical structure. It is also a great tool for stressing out aspiring biochem majors. (Reading NMR graphs is very difficult. Google it. You'll see what I mean.)

== See also ==

[http://www.physicsbook.gatech.edu/Light_Scaterring:_Why_is_the_Sky_Blue Why is the Sky Blue]

===Further reading===

Matter and Interactions Textbook (Section 23.2)

===External links===
[https://www.youtube.com/watch?v=4CtnUETLIFs Quick Animation]

[https://www.youtube.com/watch?v=d50avTf0OLw Tutor Literally Yelling Information at You (JK his voice is just loud)]

[http://imagine.gsfc.nasa.gov/science/toolbox/emspectrum1.html NASA on Electromagnetic Waves]

==References==

Matter and Interactions Textbook Section 23.2

[[Category:Radiation]]

Edited by Chiagoziem Obi

Electromagnetic Propagation

2015-12-03T02:20:07Z

ChiChiO:

Electromagnetic Propagation Model
*BY CHIAGOZIEM OBI*

==The Main Idea==

What is the ideal model for the propagation of electromagnetic waves? Does it look like a sheet of electrons? Maybe it can be described as a spring? A mountain? No! The following explains why the best model is a traveling slab of perpendicular waves that oscillate back and forth.

==A Mathematical Model: Maxwell's Equations==

===Gauss's Law for Electricity and Magnetism===
<math>\sum \phi_{electric} = \frac{q_{inside}}{\epsilon_0} = \int \vec{E} \bullet d\vec{A} </math>
<math>\sum \phi_{magnetic} = 0 = \int \vec{B} \bullet d\vec{A} </math>

===Faraday's Law===
<math> \int \vec{E} \bullet d\vec{l} = -\frac{d\phi_{magnetic}}{dt}</math>

===Ampere-Maxwell Law===
<math> \int \vec{B} \bullet d\vec{l} = \mu_0\epsilon_0\frac{d\phi_{electric}}{dt} + \mu_0I_{enclosed}</math>

==An Interactive Computational Model==

Follow this link to find an interesting little animation.

http://www.walter-fendt.de/ph14e/emwave.htm

==Proposed Model==

Waves may be a familiar concept. We can imagine waves as the familiar up-and-down movement of crests and troughs. The concept of a wave is also applicable to the physics of radiation. According to Maxwell’s equations, a time varying electric field produces a magnetic field, just as a time varying electric field produces a magnetic field. We can try to picture what such a time varying field would “look” like. Let’s propose a model for it.

We can call this single traveling box of field a pulse. There are no charges inside or outside of it. It is simply a traveling box of electric field. It generates a perpendicular magnetic field. Both electric field and magnetic field are perpendicular to the direction that the fields are moving. We can call this a “pulse” of electromagnetic field.

In order to be an acceptable model, it must satisfy all four of the equations of Maxwell. Applying Guass’s law for electricity and magnetism we see that the model works out.

===Does the Model Fit the Math?===

===Gauss's Law===
Lets use the slab as a Gauss surface. Calculate the flux through the surface. Applying Gauss' Law shows us that since there is equal amounts of magnetic and electric flux going into and out of the slab, there is no net charge or magnetic monopole through the slab.
[[File:Gauss_Electric.jpg]]
[[File:Gauss_Magnetic.jpg]]

===Faraday's Law===
Applying Faraday’s law involves realizing that the pulse in moving through space, and, for an imaginary path, the flux is changing through that path. We can pick a path h high and w wide, and allow part of the path to be inside the box of pulse and some of the path to be outside the pulse, initially. A short time, Δt, later the pulse has moved, encompassing more of the path. The change in the flux is the magnitude of the magnetic field times the velocity of the particle times the height of the path.
The change in flux is equal to the emf around the path. The electric field times the height is equal to the emf. So Eh = Bvh. Simplifying that solution yields that the electric field is equal to the velocity times the magnetic field.

===Ampere-Maxwell Law===

This law states that the magnetic field times the path length is equal to <math>\mu_0 \sum I_{enclosed}+ \frac{d\phi_{electric}}{dt}\mu_0\epsilon_0</math> The change in electric flux is equal to Evh. The magnetic field integral is Bh. Equating the two yields that <math>\mu_0\epsilon_0Evh = Bh </math> Simplifying yields that <math> B = \mu_0\epsilon_0vE</math>
So using our model of a box-like particle and applying Ampere-Maxwell’s equations to it, we’ve found that <math> E = vB </math> and <math> B = \mu_0\epsilon_0vE </math> Also the electric flux and magnetic flux equal zero. Solving for v we find that v = 3e8 m/s. This is the speed of light.

==Connectedness==
This model of electromagnetic waves allows us to predict the effects of light and other waves on matter. We know that light can be polarized into one direction, which is practical for use in optics. We also can determine the interaction between these waves and charged particles. For instance, one important idea is that electromagnetic waves carry energy. Chemists use the properties of light energy in techniques called spectroscopy. Magnetic and electric waves and fields are critical in determining structure of unknown molecules.

===History of Application===

One historical application is Nuclear magnetic resonance (NMR) imaging of chemical substances to determine structure. A sample is exposed to powerful magnetic fields, in order to align the particles. Magnetic spins of the electrons of the Hydrogen atoms. They align in the most favorable (lowest energy) alignment. Then the sample is blasting with varying frequencies of electric field (up to 300million Hz) and the frequency at which the electrons move out of alignment is recorded. This information is then used to determine structures of molecules. (Can you tell that I'm a biochem major?)

The application of this method stems from the understanding of how these waves interact with the charged particles of matter. Our models for atoms and electromagnetic waves allow us to make useful and accurate predictions about chemical structure. It is also a great tool for stressing out aspiring biochem majors. (Reading NMR graphs is very difficult. Google it. You'll see what I mean.)

== See also ==

[http://www.physicsbook.gatech.edu/Light_Scaterring:_Why_is_the_Sky_Blue Why is the Sky Blue]

===Further reading===

Matter and Interactions Textbook (Section 23.2)

===External links===
[https://www.youtube.com/watch?v=4CtnUETLIFs Quick Animation]

[https://www.youtube.com/watch?v=d50avTf0OLw Tutor Literally Yelling Information at You (JK his voice is just loud)]

[http://imagine.gsfc.nasa.gov/science/toolbox/emspectrum1.html NASA on Electromagnetic Waves]

==References==

Matter and Interactions Textbook Section 23.2

[[Category:Radiation]]

Edited by Chiagoziem Obi

File:Gauss Electric.JPG

2015-12-03T02:17:58Z

ChiChiO:

File:Gauss Magnetic.JPG

2015-12-03T02:17:41Z

ChiChiO:

2015-12-02T16:58:05Z

ChiChiO: Model for Waves

Electromagnetic Propagation Model

==The Main Idea==

What is the ideal model for the propagation of electromagnetic waves? Does it look like a sheet of electrons? Maybe it can be described as a spring? A mountain? No! The following explains why the best model is a traveling slab of perpendicular waves that oscillate back and forth.

===A Mathematical Model===

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===

===Introduction===

Waves may be a familiar concept. We can imagine waves as the familiar up-and-down movement of crests and troughs. The concept of a wave is also applicable to the physics of radiation. According to Maxwell’s equations, a time varying electric field produces a magnetic field, just as a time varying electric field produces a magnetic field. We can try to picture what such a time varying field would “look” like. Let’s propose a model for it.

We can call this single traveling box of field a pulse. There are no charges inside or outside of it. It is simply a traveling box of electric field. It generates a perpendicular magnetic field. Both electric field and magnetic field are perpendicular to the direction that the fields are moving. We can call this a “pulse” of electromagnetic field.

In order to be an acceptable model, it must satisfy all four of the equations of Maxwell. Applying Guass’s law for electricity and magnetism we see that the model works out.

===Mathematical Principles===

===Gauss's Law===

===Faraday's Law===
Applying Faraday’s law involves realizing that the pulse in moving through space, and, for an imaginary path, the flux is changing through that path. We can pick a path h high and w wide, and allow part of the path to be inside the box of pulse and some of the path to be outside the pulse, initially. A short time, Δt, later the pulse has moved, encompassing more of the path. The change in the flux is the magnitude of the magnetic field times the velocity of the particle times the height of the path.
The change in flux is equal to the emf around the path. The electric field times the height is equal to the emf. So Eh = Bvh. Simplifying that solution yields that the electric field is equal to the velocity times the magnetic field.

===Ampere-Maxwell Law===

This law states that the magnetic field times the path length is equal to mu naught times the quantity of the sum of currents inside the path plus the change in electric flux times epsilon naught. The change in electric flux is equal to Evh. The magnetic field integral is Bh. Equating the two yields that mu naught, epsilon naughtEvh is equal to Bh. Simplifying yields that B = mu naught epislon naught vE.
So using our model of a box-like particle and applying Maxwell’s equations to it, we’ve found that E = vB and B = mu epsilongVE. Also the electric flux and magnetic flux equal zero. Solving for v we find that v = 3e8 m/s. This is the speed of light.

===Difficult===

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== 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===

Internet resources on this topic

==References==

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

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

Edited by Chiagoziem Obi

Main Page

2015-11-28T20:18:12Z

ChiChiO: /* Radiation */