Physics Book - User contributions [en]

Maxwell's Electromagnetic Theory

2018-04-19T00:19:22Z

Dsaracino3:

Claimed by Griffin Bonnett Spring 2017. Edited by Danielle Saracino Spring 2018.

Written by Megan Sales. Edited by Grace Newville.

A general description of "A Dynamical Theory of the Electromagnetic Field," proposed by Maxwell in 1865.

==The Main Idea==

"''Light consists in transverse undulations of the same medium which is the cause of electric and magnetic oscillations''" - James Maxwell

In short, Maxwell suggested that light, an electric field, and a magnetic field could all be explained in a single electromagnetic theory. Maxwell’s theory describes that the electric and magnetic fields which were once thought to be two separate fields are actually distinctly different, paired components of the '''same''' field. James Clerk Maxwell developed his theory, with the help of Einstein's prior special relativity theory, that brought together two of the main concepts discussed in this class: electric fields and magnetic fields. These fields have largely been discussed separately, but when Maxwell's Equations were first introduced, the connections became more and more apparent. Maxwell's Electromagnetic Theory brought about the deep relation between electric and magnetic fields, i.e. electromagnetic fields. Maxwell's theory proposed that electric and magnetic fields move as waves at the speed of light. This was the first time electricity, magnetism, and light had been related in such a way. Together, the four equations give a complete description of all of the spatial patters of magnetic and electric fields that are possible anywhere in space for many different varying scenarios.

Brief Overview of Maxwell's Electromagnetic Theory:
https://www.youtube.com/watch?v=50v75xPfhQI

===A Mathematical Model===

Maxwell Equations:

[[File:Maxwell-review.gif]]

These are the four complete Maxwell Equations in their integral form.

1) Gauss's Law relates electric field to the charge enclosed by a "Gaussian Surface." The integral represents the sum of electric flux, so by finding this and multiplying by epsilon-zero, the charge enclosed by the surface may be calculated. The electric flux out of any closed surface is proportional to the total charge enclosed within the surface.

2) Gauss's Law for magnetism states that the sum of magnetic flux for a specific area is equal to zero. This amounts to a statement about the sources of magnetic field. For a magnetic dipole, any closed surface the magnetic flux directed inward toward the south pole will equal the flux outward from the north pole.

3) Faraday's Law directly relates electric and magnetic fields by being able to find the non-Coulomb Electric field that is produced due to a magnetic field and current. The line integral of the electric field around a closed loop is equal to the negative of the rate of change of the magnetic flux through the area enclosed by the loop.

4) Ampere-Maxwell Law is perhaps the most complex of Maxwell's Equations, and involves the derivative of electric flux. In the case of static electric field, the line integral of the magnetic field around a closed loop is proportional to the electric current flowing through the loop.

[[File:Maxwell_equation.jpg]]

[[File:Maxwellunits123.jpg]]

This is the four complete Maxwell Equations in their differential form.

===A Computational Model===

Maxwell's equations can be used to model a multitude of scenarios, but the key idea is that a time-varying magnetic field is associated with an electric field and vice versa. This leads to the concept that by solving the partial differential equations given by these four equations, all fields traveling through space may be modeled, but for most cases the calculations are so complex that they must be done computationally.

Check out [http://www.matterandinteractions.org/student/Mechanics/LectureVideos/Content/Ch23.html this resource] for several interesting demonstrations.

==Examples==

===Gauss's Law Example===

https://www.youtube.com/watch?v=c0S7U6uldsc

===Derivation===

Lengthy, but very informative:

https://www.youtube.com/watch?v=AWI70HXrbG0

==Connectedness==

Maxwell’s theory proved that electric and magnetic forces are not seperate, but different versions of the same thing, the electromagnetic force. This became a motivation to attempt to unify the four basic forces in nature—the gravitational, electrical, strong, and weak nuclear forces.

Although changing electric fields create relatively weak magnetic fields that could not be detected during Maxwell’s lifetime, he realized they existed.He predicted that these changing fields would propagate from the source like waves generated on a lake by a jumping fish. Maxwell concluded that light is an electromagnetic wave having such wavelengths that it can be detected by the eye.

This [https://www.youtube.com/watch?v=UDetOBm9RUs video] shows the derivation of the equations for thermodynamics, something a lot of students will use here at Georgia Tech if they take Thermodynamics.

Maxwell's equations also have a direct industrial application. They are used in magnetic machines and to accurately predict electrical machine performance. They also led to the development of the [https://en.wikipedia.org/wiki/Maxwell_stress_tensor Maxwell stress tensor].

==History==
While in Copenhagen in 1820 Hans Christian Oersted embarked on a series of experiments in which he hoped to connect magnetism and electricity. This became an early inspiration for Maxwell’s work as well as many other physicists hoping to discover the fundamental nature of this “mysterious connection.”

A decade after Oersted’s experiment, Michael Faraday successfully converted electric energy into magnetic energy using an insulated wire and a galvanometer. This experiment was later used in a paper ‘On Faraday’s Lines of Force’ which derived electric and magnetic equations by comparing the flow of liquid to lines of electrical and magnetic force.

When James Clerk Maxwell came out with his paper, "A dynamical theory of the electromagnetic field," in 1865, it was found hard to understand and widely ignored. Even so, it is one of the most important pieces of theory in our history. He himself downplayed the importance of his theory, putting more emphasis on Kelvin's vortex theory during his own address. Furthermore, it was hard to grasp the concept of intangible fields. Scientists, including Maxwell, tried to picture fields as tangible structures, but to use these mechanical models with the Maxwell equations, they had to be exceedingly complicated. Later, other physicists such as Hertz, Lorentz, and Einstein clarified his theory.

When the paper first was written, it was read to the Royal Society. It was next read and reviewed by many other notable physicists, all prior to its publication. Even once it was published, very few copies were produced.

There were originally 20 equations. These were reduced by Heaviside into 8 equations, and these later became the four equations we are familiar with.

===Impact===

Maxwell was the first to show how to calculate stresses in framed arch and suspension bridges.

He invented the term "curl" for the vector operator that appears in his equations for the electromagnetic field.

Maxwell postulated that light is a form of electromagnetic radiation exerting pressure and carrying momentum. He provided the basis for Einstein's work on relativity from which the relationship between energy, mass and velocity contributed to the theory underlying the development of atomic energy.

Maxwell made fundamental contributions to the development of thermodynamics. He was also a founder of the kinetic theory of gases. This theory provided the new subject of statistical physics, linking thermodynamics and mechanics, and is still widely used as a model for rarefied gases and plasmas.

The discovery of electromagnetic radiation led to the development of radio and infra-red telescopes, currently exploring the farthest reaches of space.

==Timeline of Maxwell's Contributions==

'''1885''' - Oliver Heaviside simplifies the Maxwell equations to the ones used today.

'''1897''' - Guglielmo Marcon employs electromagnetic waves for radio communications.

'''1905''' - Albert Einstein uses the Maxwell equations to start his famous theory of special relativity.

'''1920''' - Homes began to use radio to listen to music and voice.

'''1957''' - Sony begins mass producing affordable transistor radios.

'''1973''' - First handheld or cellular mobile telephone networks.

'''2000''' - WiFi expands connectivity of mobile devices to the internet.

[[File:Maxwell3597.jpg]]

== See also ==

[[James Maxwell]]

[[ Maxwell's Equations]]

===Further reading===

The theory itself:

http://www.ymambrini.com/My_World/History_files/maxwell_emf_1865.pdf

==References==

http://www.damtp.cam.ac.uk/user/tong/em/dyson.pdf

http://rsta.royalsocietypublishing.org/content/366/1871/1807

http://silas.psfc.mit.edu/maxwell/

http://www.clerkmaxwellfoundation.org/html/electromagnetic_theory.html

https://www.colorado.edu/physics/phys4510/phys4510_fa05/Chapter1.pdf

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/maxeq2.html#c1

https://www.azooptics.com/Article.aspx?ArticleID=944

http://www.clerkmaxwellfoundation.org/html/maxwell-s_impact_.html

https://opentextbc.ca/physicstestbook2/chapter/maxwells-equations-electromagnetic-waves-predicted-and-observed/

[[Category: Theory]]

Maxwell's Electromagnetic Theory

2018-04-19T00:18:40Z

Dsaracino3: /* Connectedness */

Maxwell's Electromagnetic Theory

2018-04-19T00:17:15Z

Dsaracino3:

Claimed by Griffin Bonnett Spring 2017. Edited by Danielle Saracino Spring 2018.

Written by Megan Sales. Edited by Grace Newville.

A general description of "A Dynamical Theory of the Electromagnetic Field," proposed by Maxwell in 1865.

==The Main Idea==

"''Light consists in transverse undulations of the same medium which is the cause of electric and magnetic oscillations''" - James Maxwell

In short, Maxwell suggested that light, an electric field, and a magnetic field could all be explained in a single electromagnetic theory. Maxwell’s theory describes that the electric and magnetic fields which were once thought to be two separate fields are actually distinctly different, paired components of the '''same''' field. James Clerk Maxwell developed his theory, with the help of Einstein's prior special relativity theory, that brought together two of the main concepts discussed in this class: electric fields and magnetic fields. These fields have largely been discussed separately, but when Maxwell's Equations were first introduced, the connections became more and more apparent. Maxwell's Electromagnetic Theory brought about the deep relation between electric and magnetic fields, i.e. electromagnetic fields. Maxwell's theory proposed that electric and magnetic fields move as waves at the speed of light. This was the first time electricity, magnetism, and light had been related in such a way. Together, the four equations give a complete description of all of the spatial patters of magnetic and electric fields that are possible anywhere in space for many different varying scenarios.

Brief Overview of Maxwell's Electromagnetic Theory:
https://www.youtube.com/watch?v=50v75xPfhQI

===A Mathematical Model===

Maxwell Equations:

[[File:Maxwell-review.gif]]

These are the four complete Maxwell Equations in their integral form.

1) Gauss's Law relates electric field to the charge enclosed by a "Gaussian Surface." The integral represents the sum of electric flux, so by finding this and multiplying by epsilon-zero, the charge enclosed by the surface may be calculated. The electric flux out of any closed surface is proportional to the total charge enclosed within the surface.

2) Gauss's Law for magnetism states that the sum of magnetic flux for a specific area is equal to zero. This amounts to a statement about the sources of magnetic field. For a magnetic dipole, any closed surface the magnetic flux directed inward toward the south pole will equal the flux outward from the north pole.

3) Faraday's Law directly relates electric and magnetic fields by being able to find the non-Coulomb Electric field that is produced due to a magnetic field and current. The line integral of the electric field around a closed loop is equal to the negative of the rate of change of the magnetic flux through the area enclosed by the loop.

4) Ampere-Maxwell Law is perhaps the most complex of Maxwell's Equations, and involves the derivative of electric flux. In the case of static electric field, the line integral of the magnetic field around a closed loop is proportional to the electric current flowing through the loop.

[[File:Maxwell_equation.jpg]]

[[File:Maxwellunits123.jpg]]

This is the four complete Maxwell Equations in their differential form.

===A Computational Model===

Maxwell's equations can be used to model a multitude of scenarios, but the key idea is that a time-varying magnetic field is associated with an electric field and vice versa. This leads to the concept that by solving the partial differential equations given by these four equations, all fields traveling through space may be modeled, but for most cases the calculations are so complex that they must be done computationally.

Check out [http://www.matterandinteractions.org/student/Mechanics/LectureVideos/Content/Ch23.html this resource] for several interesting demonstrations.

==Examples==

===Gauss's Law Example===

https://www.youtube.com/watch?v=c0S7U6uldsc

===Derivation===

Lengthy, but very informative:

https://www.youtube.com/watch?v=AWI70HXrbG0

==Connectedness==

Maxwell’s theory proved that electric and magnetic forces are not seperate, but different versions of the same thing, the electromagnetic force. This became a motivation to attempt to unify the four basic forces in nature—the gravitational, electrical, strong, and weak nuclear forces.

Although changing electric fields create relatively weak magnetic fields that could not be detected during Maxwell’s lifetime, he realized they existed.He predicted that these changing fields would propagate from the source like waves generated on a lake by a jumping fish. Maxwell concluded that light is an electromagnetic wave having such wavelengths that it can be detected by the eye.

==History==
While in Copenhagen in 1820 Hans Christian Oersted embarked on a series of experiments in which he hoped to connect magnetism and electricity. This became an early inspiration for Maxwell’s work as well as many other physicists hoping to discover the fundamental nature of this “mysterious connection.”

A decade after Oersted’s experiment, Michael Faraday successfully converted electric energy into magnetic energy using an insulated wire and a galvanometer. This experiment was later used in a paper ‘On Faraday’s Lines of Force’ which derived electric and magnetic equations by comparing the flow of liquid to lines of electrical and magnetic force.

When James Clerk Maxwell came out with his paper, "A dynamical theory of the electromagnetic field," in 1865, it was found hard to understand and widely ignored. Even so, it is one of the most important pieces of theory in our history. He himself downplayed the importance of his theory, putting more emphasis on Kelvin's vortex theory during his own address. Furthermore, it was hard to grasp the concept of intangible fields. Scientists, including Maxwell, tried to picture fields as tangible structures, but to use these mechanical models with the Maxwell equations, they had to be exceedingly complicated. Later, other physicists such as Hertz, Lorentz, and Einstein clarified his theory.

When the paper first was written, it was read to the Royal Society. It was next read and reviewed by many other notable physicists, all prior to its publication. Even once it was published, very few copies were produced.

There were originally 20 equations. These were reduced by Heaviside into 8 equations, and these later became the four equations we are familiar with.

===Impact===

Maxwell was the first to show how to calculate stresses in framed arch and suspension bridges.

He invented the term "curl" for the vector operator that appears in his equations for the electromagnetic field.

Maxwell postulated that light is a form of electromagnetic radiation exerting pressure and carrying momentum. He provided the basis for Einstein's work on relativity from which the relationship between energy, mass and velocity contributed to the theory underlying the development of atomic energy.

Maxwell made fundamental contributions to the development of thermodynamics. He was also a founder of the kinetic theory of gases. This theory provided the new subject of statistical physics, linking thermodynamics and mechanics, and is still widely used as a model for rarefied gases and plasmas.

The discovery of electromagnetic radiation led to the development of radio and infra-red telescopes, currently exploring the farthest reaches of space.

==Timeline of Maxwell's Contributions==

'''1885''' - Oliver Heaviside simplifies the Maxwell equations to the ones used today.

'''1897''' - Guglielmo Marcon employs electromagnetic waves for radio communications.

'''1905''' - Albert Einstein uses the Maxwell equations to start his famous theory of special relativity.

'''1920''' - Homes began to use radio to listen to music and voice.

'''1957''' - Sony begins mass producing affordable transistor radios.

'''1973''' - First handheld or cellular mobile telephone networks.

'''2000''' - WiFi expands connectivity of mobile devices to the internet.

[[File:Maxwell3597.jpg]]

== See also ==

[[James Maxwell]]

[[ Maxwell's Equations]]

===Further reading===

The theory itself:

http://www.ymambrini.com/My_World/History_files/maxwell_emf_1865.pdf

==References==

http://www.damtp.cam.ac.uk/user/tong/em/dyson.pdf

http://rsta.royalsocietypublishing.org/content/366/1871/1807

http://silas.psfc.mit.edu/maxwell/

http://www.clerkmaxwellfoundation.org/html/electromagnetic_theory.html

https://www.colorado.edu/physics/phys4510/phys4510_fa05/Chapter1.pdf

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/maxeq2.html#c1

https://www.azooptics.com/Article.aspx?ArticleID=944

http://www.clerkmaxwellfoundation.org/html/maxwell-s_impact_.html

[[Category: Theory]]

Maxwell's Electromagnetic Theory

2018-04-19T00:16:52Z

Dsaracino3:

Claimed by Griffin Bonnett Spring 2017. Edited by Danielle Saracino Spring 2018.

Written by Megan Sales. Edited by Grace Newville.

A general description of "A Dynamical Theory of the Electromagnetic Field," proposed by Maxwell in 1865.

==The Main Idea==

"''Light consists in transverse undulations of the same medium which is the cause of electric and magnetic oscillations''" - James Maxwell

In short, Maxwell suggested that light, an electric field, and a magnetic field could all be explained in a single electromagnetic theory. Maxwell’s theory describes that the electric and magnetic fields which were once thought to be two separate fields are actually distinctly different, paired components of the '''same''' field. James Clerk Maxwell developed his theory, with the help of Einstein's prior special relativity theory, that brought together two of the main concepts discussed in this class: electric fields and magnetic fields. These fields have largely been discussed separately, but when Maxwell's Equations were first introduced, the connections became more and more apparent. Maxwell's Electromagnetic Theory brought about the deep relation between electric and magnetic fields, i.e. electromagnetic fields. Maxwell's theory proposed that electric and magnetic fields move as waves at the speed of light. This was the first time electricity, magnetism, and light had been related in such a way. Together, the four equations give a complete description of all of the spatial patters of magnetic and electric fields that are possible anywhere in space for many different varying scenarios.

Brief Overview of Maxwell's Electromagnetic Theory:
https://www.youtube.com/watch?v=50v75xPfhQI

===A Mathematical Model===

Maxwell Equations:

[[File:Maxwell-review.gif]]

These are the four complete Maxwell Equations in their integral form.

1) Gauss's Law relates electric field to the charge enclosed by a "Gaussian Surface." The integral represents the sum of electric flux, so by finding this and multiplying by epsilon-zero, the charge enclosed by the surface may be calculated. The electric flux out of any closed surface is proportional to the total charge enclosed within the surface.

2) Gauss's Law for magnetism states that the sum of magnetic flux for a specific area is equal to zero. This amounts to a statement about the sources of magnetic field. For a magnetic dipole, any closed surface the magnetic flux directed inward toward the south pole will equal the flux outward from the north pole.

3) Faraday's Law directly relates electric and magnetic fields by being able to find the non-Coulomb Electric field that is produced due to a magnetic field and current. The line integral of the electric field around a closed loop is equal to the negative of the rate of change of the magnetic flux through the area enclosed by the loop.

4) Ampere-Maxwell Law is perhaps the most complex of Maxwell's Equations, and involves the derivative of electric flux. In the case of static electric field, the line integral of the magnetic field around a closed loop is proportional to the electric current flowing through the loop.

[[File:Maxwell_equation.jpg]]

[[File:Maxwellunits123.jpg]]

This is the four complete Maxwell Equations in their differential form.

===A Computational Model===

Maxwell's equations can be used to model a multitude of scenarios, but the key idea is that a time-varying magnetic field is associated with an electric field and vice versa. This leads to the concept that by solving the partial differential equations given by these four equations, all fields traveling through space may be modeled, but for most cases the calculations are so complex that they must be done computationally.

Check out [http://www.matterandinteractions.org/student/Mechanics/LectureVideos/Content/Ch23.html this resource] for several interesting demonstrations.

==Examples==

===Gauss's Law Example===

https://www.youtube.com/watch?v=c0S7U6uldsc

===Derivation===

Lengthy, but very informative:

https://www.youtube.com/watch?v=AWI70HXrbG0

==Connectedness==

==History==
While in Copenhagen in 1820 Hans Christian Oersted embarked on a series of experiments in which he hoped to connect magnetism and electricity. This became an early inspiration for Maxwell’s work as well as many other physicists hoping to discover the fundamental nature of this “mysterious connection.”

A decade after Oersted’s experiment, Michael Faraday successfully converted electric energy into magnetic energy using an insulated wire and a galvanometer. This experiment was later used in a paper ‘On Faraday’s Lines of Force’ which derived electric and magnetic equations by comparing the flow of liquid to lines of electrical and magnetic force.

When James Clerk Maxwell came out with his paper, "A dynamical theory of the electromagnetic field," in 1865, it was found hard to understand and widely ignored. Even so, it is one of the most important pieces of theory in our history. He himself downplayed the importance of his theory, putting more emphasis on Kelvin's vortex theory during his own address. Furthermore, it was hard to grasp the concept of intangible fields. Scientists, including Maxwell, tried to picture fields as tangible structures, but to use these mechanical models with the Maxwell equations, they had to be exceedingly complicated. Later, other physicists such as Hertz, Lorentz, and Einstein clarified his theory.

When the paper first was written, it was read to the Royal Society. It was next read and reviewed by many other notable physicists, all prior to its publication. Even once it was published, very few copies were produced.

There were originally 20 equations. These were reduced by Heaviside into 8 equations, and these later became the four equations we are familiar with.

===Impact===

Maxwell was the first to show how to calculate stresses in framed arch and suspension bridges.

He invented the term "curl" for the vector operator that appears in his equations for the electromagnetic field.

Maxwell postulated that light is a form of electromagnetic radiation exerting pressure and carrying momentum. He provided the basis for Einstein's work on relativity from which the relationship between energy, mass and velocity contributed to the theory underlying the development of atomic energy.

Maxwell made fundamental contributions to the development of thermodynamics. He was also a founder of the kinetic theory of gases. This theory provided the new subject of statistical physics, linking thermodynamics and mechanics, and is still widely used as a model for rarefied gases and plasmas.

The discovery of electromagnetic radiation led to the development of radio and infra-red telescopes, currently exploring the farthest reaches of space.

==Timeline of Maxwell's Contributions==

'''1885''' - Oliver Heaviside simplifies the Maxwell equations to the ones used today.

'''1897''' - Guglielmo Marcon employs electromagnetic waves for radio communications.

'''1905''' - Albert Einstein uses the Maxwell equations to start his famous theory of special relativity.

'''1920''' - Homes began to use radio to listen to music and voice.

'''1957''' - Sony begins mass producing affordable transistor radios.

'''1973''' - First handheld or cellular mobile telephone networks.

'''2000''' - WiFi expands connectivity of mobile devices to the internet.

[[File:Maxwell3597.jpg]]

== See also ==

[[James Maxwell]]

[[ Maxwell's Equations]]

===Further reading===

The theory itself:

http://www.ymambrini.com/My_World/History_files/maxwell_emf_1865.pdf

==References==

http://www.damtp.cam.ac.uk/user/tong/em/dyson.pdf

http://rsta.royalsocietypublishing.org/content/366/1871/1807

http://silas.psfc.mit.edu/maxwell/

http://www.clerkmaxwellfoundation.org/html/electromagnetic_theory.html

https://www.colorado.edu/physics/phys4510/phys4510_fa05/Chapter1.pdf

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/maxeq2.html#c1

https://www.azooptics.com/Article.aspx?ArticleID=944

http://www.clerkmaxwellfoundation.org/html/maxwell-s_impact_.html

[[Category: Theory]]

Maxwell's Electromagnetic Theory

2018-04-19T00:00:59Z

Dsaracino3:

Claimed by Griffin Bonnett Spring 2017. Edited by Danielle Saracino Spring 2018.

Written by Megan Sales. Edited by Grace Newville.

A general description of "A Dynamical Theory of the Electromagnetic Field," proposed by Maxwell in 1865.

==The Main Idea==

"''Light consists in transverse undulations of the same medium which is the cause of electric and magnetic oscillations''" - James Maxwell

In short, Maxwell suggested that light, an electric field, and a magnetic field could all be explained in a single electromagnetic theory. Maxwell’s theory describes that the electric and magnetic fields which were once thought to be two separate fields are actually distinctly different, paired components of the '''same''' field. James Clerk Maxwell developed his theory, with the help of Einstein's prior special relativity theory, that brought together two of the main concepts discussed in this class: electric fields and magnetic fields. These fields have largely been discussed separately, but when Maxwell's Equations were first introduced, the connections became more and more apparent. Maxwell's Electromagnetic Theory brought about the deep relation between electric and magnetic fields, i.e. electromagnetic fields. Maxwell's theory proposed that electric and magnetic fields move as waves at the speed of light. This was the first time electricity, magnetism, and light had been related in such a way. Together, the four equations give a complete description of all of the spatial patters of magnetic and electric fields that are possible anywhere in space for many different varying scenarios.

Brief Overview of Maxwell's Electromagnetic Theory:
https://www.youtube.com/watch?v=50v75xPfhQI

===A Mathematical Model===

Maxwell Equations:

[[File:Maxwell-review.gif]]

These are the four complete Maxwell Equations in their integral form.

1) Gauss's Law relates electric field to the charge enclosed by a "Gaussian Surface." The integral represents the sum of electric flux, so by finding this and multiplying by epsilon-zero, the charge enclosed by the surface may be calculated. The electric flux out of any closed surface is proportional to the total charge enclosed within the surface.

2) Gauss's Law for magnetism states that the sum of magnetic flux for a specific area is equal to zero. This amounts to a statement about the sources of magnetic field. For a magnetic dipole, any closed surface the magnetic flux directed inward toward the south pole will equal the flux outward from the north pole.

3) Faraday's Law directly relates electric and magnetic fields by being able to find the non-Coulomb Electric field that is produced due to a magnetic field and current. The line integral of the electric field around a closed loop is equal to the negative of the rate of change of the magnetic flux through the area enclosed by the loop.

4) Ampere-Maxwell Law is perhaps the most complex of Maxwell's Equations, and involves the derivative of electric flux. In the case of static electric field, the line integral of the magnetic field around a closed loop is proportional to the electric current flowing through the loop.

[[File:Maxwell_equation.jpg]]

[[File:Maxwellunits123.jpg]]

This is the four complete Maxwell Equations in their differential form.

===A Computational Model===

Maxwell's equations can be used to model a multitude of scenarios, but the key idea is that a time-varying magnetic field is associated with an electric field and vice versa. This leads to the concept that by solving the partial differential equations given by these four equations, all fields traveling through space may be modeled, but for most cases the calculations are so complex that they must be done computationally.

Check out [http://www.matterandinteractions.org/student/Mechanics/LectureVideos/Content/Ch23.html this resource] for several interesting demonstrations.

==Examples==

===Gauss's Law Example===

https://www.youtube.com/watch?v=c0S7U6uldsc

===Derivation===

Lengthy, but very informative:

https://www.youtube.com/watch?v=AWI70HXrbG0

==Connectedness==
I first saw Maxwell's Equations in my thermodynamics class last semester. That is what prompted me to explore the theory behind them, as I had only used them in a practical application. That being said, this [https://www.youtube.com/watch?v=UDetOBm9RUs video] shows the derivation of the equations for thermodynamics, something I use as a chemical engineer.

Maxwell's equations also have a direct industrial application. They are used in magnetic machines and to accurately predict electrical machine performance. They also led to the development of the [https://en.wikipedia.org/wiki/Maxwell_stress_tensor Maxwell stress tensor].

==History==
While in Copenhagen in 1820 Hans Christian Oersted embarked on a series of experiments in which he hoped to connect magnetism and electricity. This became an early inspiration for Maxwell’s work as well as many other physicists hoping to discover the fundamental nature of this “mysterious connection.”

A decade after Oersted’s experiment, Michael Faraday successfully converted electric energy into magnetic energy using an insulated wire and a galvanometer. This experiment was later used in a paper ‘On Faraday’s Lines of Force’ which derived electric and magnetic equations by comparing the flow of liquid to lines of electrical and magnetic force.

When James Clerk Maxwell came out with his paper, "A dynamical theory of the electromagnetic field," in 1865, it was found hard to understand and widely ignored. Even so, it is one of the most important pieces of theory in our history. He himself downplayed the importance of his theory, putting more emphasis on Kelvin's vortex theory during his own address. Furthermore, it was hard to grasp the concept of intangible fields. Scientists, including Maxwell, tried to picture fields as tangible structures, but to use these mechanical models with the Maxwell equations, they had to be exceedingly complicated. Later, other physicists such as Hertz, Lorentz, and Einstein clarified his theory.

When the paper first was written, it was read to the Royal Society. It was next read and reviewed by many other notable physicists, all prior to its publication. Even once it was published, very few copies were produced.

There were originally 20 equations. These were reduced by Heaviside into 8 equations, and these later became the four equations we are familiar with.

===Impact===

Maxwell was the first to show how to calculate stresses in framed arch and suspension bridges.

He invented the term "curl" for the vector operator that appears in his equations for the electromagnetic field.

Maxwell postulated that light is a form of electromagnetic radiation exerting pressure and carrying momentum. He provided the basis for Einstein's work on relativity from which the relationship between energy, mass and velocity contributed to the theory underlying the development of atomic energy.

Maxwell made fundamental contributions to the development of thermodynamics. He was also a founder of the kinetic theory of gases. This theory provided the new subject of statistical physics, linking thermodynamics and mechanics, and is still widely used as a model for rarefied gases and plasmas.

The discovery of electromagnetic radiation led to the development of radio and infra-red telescopes, currently exploring the farthest reaches of space.

==Timeline of Maxwell's Contributions==

'''1885''' - Oliver Heaviside simplifies the Maxwell equations to the ones used today.

'''1897''' - Guglielmo Marcon employs electromagnetic waves for radio communications.

'''1905''' - Albert Einstein uses the Maxwell equations to start his famous theory of special relativity.

'''1920''' - Homes began to use radio to listen to music and voice.

'''1957''' - Sony begins mass producing affordable transistor radios.

'''1973''' - First handheld or cellular mobile telephone networks.

'''2000''' - WiFi expands connectivity of mobile devices to the internet.

[[File:Maxwell3597.jpg]]

== See also ==

[[James Maxwell]]

[[ Maxwell's Equations]]

===Further reading===

The theory itself:

http://www.ymambrini.com/My_World/History_files/maxwell_emf_1865.pdf

==References==

http://www.damtp.cam.ac.uk/user/tong/em/dyson.pdf

http://rsta.royalsocietypublishing.org/content/366/1871/1807

http://silas.psfc.mit.edu/maxwell/

http://www.clerkmaxwellfoundation.org/html/electromagnetic_theory.html

https://www.colorado.edu/physics/phys4510/phys4510_fa05/Chapter1.pdf

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/maxeq2.html#c1

https://www.azooptics.com/Article.aspx?ArticleID=944

http://www.clerkmaxwellfoundation.org/html/maxwell-s_impact_.html

[[Category: Theory]]

Maxwell's Electromagnetic Theory

2018-04-19T00:00:14Z

Dsaracino3:

Claimed by Griffin Bonnett Spring 2017. Edited by Danielle Saracino Spring 2018.

Written by Megan Sales. Edited by Grace Newville.

A general description of "A Dynamical Theory of the Electromagnetic Field," proposed by Maxwell in 1865.

==The Main Idea==

"''Light consists in transverse undulations of the same medium which is the cause of electric and magnetic oscillations''" - James Maxwell

In short, Maxwell suggested that light, an electric field, and a magnetic field could all be explained in a single electromagnetic theory. Maxwell’s theory describes that the electric and magnetic fields which were once thought to be two separate fields are actually distinctly different, paired components of the '''same''' field. James Clerk Maxwell developed his theory, with the help of Einstein's prior special relativity theory, that brought together two of the main concepts discussed in this class: electric fields and magnetic fields. These fields have largely been discussed separately, but when Maxwell's Equations were first introduced, the connections became more and more apparent. Maxwell's Electromagnetic Theory brought about the deep relation between electric and magnetic fields, i.e. electromagnetic fields. Maxwell's theory proposed that electric and magnetic fields move as waves at the speed of light. This was the first time electricity, magnetism, and light had been related in such a way. Together, the four equations give a complete description of all of the spatial patters of magnetic and electric fields that are possible anywhere in space for many different varying scenarios.

Brief Overview of Maxwell's Electromagnetic Theory:
https://www.youtube.com/watch?v=50v75xPfhQI

===A Mathematical Model===

Maxwell Equations:

[[File:Maxwell-review.gif]]

These are the four complete Maxwell Equations in their integral form.

1) Gauss's Law relates electric field to the charge enclosed by a "Gaussian Surface." The integral represents the sum of electric flux, so by finding this and multiplying by epsilon-zero, the charge enclosed by the surface may be calculated. The electric flux out of any closed surface is proportional to the total charge enclosed within the surface.

2) Gauss's Law for magnetism states that the sum of magnetic flux for a specific area is equal to zero. This amounts to a statement about the sources of magnetic field. For a magnetic dipole, any closed surface the magnetic flux directed inward toward the south pole will equal the flux outward from the north pole.

3) Faraday's Law directly relates electric and magnetic fields by being able to find the non-Coulomb Electric field that is produced due to a magnetic field and current. The line integral of the electric field around a closed loop is equal to the negative of the rate of change of the magnetic flux through the area enclosed by the loop.

4) Ampere-Maxwell Law is perhaps the most complex of Maxwell's Equations, and involves the derivative of electric flux. In the case of static electric field, the line integral of the magnetic field around a closed loop is proportional to the electric current flowing through the loop.

[[File:Maxwell_equation.jpg]]

[[File:Maxwellunits123.jpg]]

This is the four complete Maxwell Equations in their differential form.

===A Computational Model===

Maxwell's equations can be used to model a multitude of scenarios, but the key idea is that a time-varying magnetic field is associated with an electric field and vice versa. This leads to the concept that by solving the partial differential equations given by these four equations, all fields traveling through space may be modeled, but for most cases the calculations are so complex that they must be done computationally.

Check out [http://www.matterandinteractions.org/student/Mechanics/LectureVideos/Content/Ch23.html this resource] for several interesting demonstrations.

==Examples==

===Gauss's Law Example===

https://www.youtube.com/watch?v=c0S7U6uldsc

===Derivation===

Lengthy, but very informative:

https://www.youtube.com/watch?v=AWI70HXrbG0

==Connectedness==
I first saw Maxwell's Equations in my thermodynamics class last semester. That is what prompted me to explore the theory behind them, as I had only used them in a practical application. That being said, this [https://www.youtube.com/watch?v=UDetOBm9RUs video] shows the derivation of the equations for thermodynamics, something I use as a chemical engineer.

Maxwell's equations also have a direct industrial application. They are used in magnetic machines and to accurately predict electrical machine performance. They also led to the development of the [https://en.wikipedia.org/wiki/Maxwell_stress_tensor Maxwell stress tensor].

==History==
While in Copenhagen in 1820 Hans Christian Oersted embarked on a series of experiments in which he hoped to connect magnetism and electricity. This became an early inspiration for Maxwell’s work as well as many other physicists hoping to discover the fundamental nature of this “mysterious connection.”

A decade after Oersted’s experiment, Michael Faraday successfully converted electric energy into magnetic energy using an insulated wire and a galvanometer. This experiment was later used in a paper ‘On Faraday’s Lines of Force’ which derived electric and magnetic equations by comparing the flow of liquid to lines of electrical and magnetic force.

When James Clerk Maxwell came out with his paper, "A dynamical theory of the electromagnetic field," in 1865, it was found hard to understand and widely ignored. Even so, it is one of the most important pieces of theory in our history. He himself downplayed the importance of his theory, putting more emphasis on Kelvin's vortex theory during his own address. Furthermore, it was hard to grasp the concept of intangible fields. Scientists, including Maxwell, tried to picture fields as tangible structures, but to use these mechanical models with the Maxwell equations, they had to be exceedingly complicated. Later, other physicists such as Hertz, Lorentz, and Einstein clarified his theory.

When the paper first was written, it was read to the Royal Society. It was next read and reviewed by many other notable physicists, all prior to its publication. Even once it was published, very few copies were produced.

There were originally 20 equations. These were reduced by Heaviside into 8 equations, and these later became the four equations we are familiar with.

===Impact===

Maxwell was the first to show how to calculate stresses in framed arch and suspension bridges.

He invented the term "curl" for the vector operator that appears in his equations for the electromagnetic field.

Maxwell postulated that light is a form of electromagnetic radiation exerting pressure and carrying momentum. He provided the basis for Einstein's work on relativity from which the relationship between energy, mass and velocity contributed to the theory underlying the development of atomic energy.

Maxwell made fundamental contributions to the development of thermodynamics. He was also a founder of the kinetic theory of gases. This theory provided the new subject of statistical physics, linking thermodynamics and mechanics, and is still widely used as a model for rarefied gases and plasmas.

The discovery of electromagnetic radiation led to the development of radio and infra-red telescopes, currently exploring the farthest reaches of space.

==Timeline of Maxwell's Contributions==

'''1885''' - Oliver Heaviside simplifies the Maxwell equations to the ones used today.

'''1897''' - Guglielmo Marcon employs electromagnetic waves for radio communications.

'''1905''' - Albert Einstein uses the Maxwell equations to start his famous theory of special relativity.

'''1920''' - Homes began to use radio to listen to music and voice.

'''1957''' - Sony begins mass producing affordable transistor radios.

'''1973''' - First handheld or cellular mobile telephone networks.

'''2000''' - WiFi expands connectivity of mobile devices to the internet.

[[File:Maxwell3597.jpg]]

== See also ==

[[James Maxwell]]

[[ Maxwell's Equations]]

===Further reading===

The theory itself:

http://www.ymambrini.com/My_World/History_files/maxwell_emf_1865.pdf

==References==

http://www.damtp.cam.ac.uk/user/tong/em/dyson.pdf

http://rsta.royalsocietypublishing.org/content/366/1871/1807

http://silas.psfc.mit.edu/maxwell/

http://www.clerkmaxwellfoundation.org/html/electromagnetic_theory.html

https://www.colorado.edu/physics/phys4510/phys4510_fa05/Chapter1.pdf

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/maxeq2.html#c1

https://www.azooptics.com/Article.aspx?ArticleID=944

[[Category: Theory]]

Maxwell's Electromagnetic Theory

2018-04-18T23:50:45Z

Dsaracino3:

Claimed by Griffin Bonnett Spring 2017. Edited by Danielle Saracino Spring 2018.

Written by Megan Sales. Edited by Grace Newville.

A general description of "A Dynamical Theory of the Electromagnetic Field," proposed by Maxwell in 1865.

==The Main Idea==

"''Light consists in transverse undulations of the same medium which is the cause of electric and magnetic oscillations''" - James Maxwell

In short, Maxwell suggested that light, an electric field, and a magnetic field could all be explained in a single electromagnetic theory. Maxwell’s theory describes that the electric and magnetic fields which were once thought to be two separate fields are actually distinctly different, paired components of the '''same''' field. James Clerk Maxwell developed his theory, with the help of Einstein's prior special relativity theory, that brought together two of the main concepts discussed in this class: electric fields and magnetic fields. These fields have largely been discussed separately, but when Maxwell's Equations were first introduced, the connections became more and more apparent. Maxwell's Electromagnetic Theory brought about the deep relation between electric and magnetic fields, i.e. electromagnetic fields. Maxwell's theory proposed that electric and magnetic fields move as waves at the speed of light. This was the first time electricity, magnetism, and light had been related in such a way. Together, the four equations give a complete description of all of the spatial patters of magnetic and electric fields that are possible anywhere in space for many different varying scenarios.

Brief Overview of Maxwell's Electromagnetic Theory:
https://www.youtube.com/watch?v=50v75xPfhQI

===A Mathematical Model===

Maxwell Equations:

[[File:Maxwell-review.gif]]

These are the four complete Maxwell Equations in their integral form.

1) Gauss's Law relates electric field to the charge enclosed by a "Gaussian Surface." The integral represents the sum of electric flux, so by finding this and multiplying by epsilon-zero, the charge enclosed by the surface may be calculated. The electric flux out of any closed surface is proportional to the total charge enclosed within the surface.

2) Gauss's Law for magnetism states that the sum of magnetic flux for a specific area is equal to zero. This amounts to a statement about the sources of magnetic field. For a magnetic dipole, any closed surface the magnetic flux directed inward toward the south pole will equal the flux outward from the north pole.

3) Faraday's Law directly relates electric and magnetic fields by being able to find the non-Coulomb Electric field that is produced due to a magnetic field and current. The line integral of the electric field around a closed loop is equal to the negative of the rate of change of the magnetic flux through the area enclosed by the loop.

4) Ampere-Maxwell Law is perhaps the most complex of Maxwell's Equations, and involves the derivative of electric flux. In the case of static electric field, the line integral of the magnetic field around a closed loop is proportional to the electric current flowing through the loop.

[[File:Maxwell_equation.jpg]]

[[File:Maxwellunits123.jpg]]

This is the four complete Maxwell Equations in their differential form.

===A Computational Model===

Maxwell's equations can be used to model a multitude of scenarios, but the key idea is that a time-varying magnetic field is associated with an electric field and vice versa. This leads to the concept that by solving the partial differential equations given by these four equations, all fields traveling through space may be modeled, but for most cases the calculations are so complex that they must be done computationally.

Check out [http://www.matterandinteractions.org/student/Mechanics/LectureVideos/Content/Ch23.html this resource] for several interesting demonstrations.

==Examples==

===Gauss's Law Example===

https://www.youtube.com/watch?v=c0S7U6uldsc

===Derivation===

Lengthy, but very informative:

https://www.youtube.com/watch?v=AWI70HXrbG0

==Connectedness==
I first saw Maxwell's Equations in my thermodynamics class last semester. That is what prompted me to explore the theory behind them, as I had only used them in a practical application. That being said, this [https://www.youtube.com/watch?v=UDetOBm9RUs video] shows the derivation of the equations for thermodynamics, something I use as a chemical engineer.

Maxwell's equations also have a direct industrial application. They are used in magnetic machines and to accurately predict electrical machine performance. They also led to the development of the [https://en.wikipedia.org/wiki/Maxwell_stress_tensor Maxwell stress tensor].

==History==
While in Copenhagen in 1820 Hans Christian Oersted embarked on a series of experiments in which he hoped to connect magnetism and electricity. This became an early inspiration for Maxwell’s work as well as many other physicists hoping to discover the fundamental nature of this “mysterious connection.”

A decade after Oersted’s experiment, Michael Faraday successfully converted electric energy into magnetic energy using an insulated wire and a galvanometer. This experiment was later used in a paper ‘On Faraday’s Lines of Force’ which derived electric and magnetic equations by comparing the flow of liquid to lines of electrical and magnetic force.

When James Clerk Maxwell came out with his paper, "A dynamical theory of the electromagnetic field," in 1865, it was found hard to understand and widely ignored. Even so, it is one of the most important pieces of theory in our history. He himself downplayed the importance of his theory, putting more emphasis on Kelvin's vortex theory during his own address. Furthermore, it was hard to grasp the concept of intangible fields. Scientists, including Maxwell, tried to picture fields as tangible structures, but to use these mechanical models with the Maxwell equations, they had to be exceedingly complicated. Later, other physicists such as Hertz, Lorentz, and Einstein clarified his theory.

When the paper first was written, it was read to the Royal Society. It was next read and reviewed by many other notable physicists, all prior to its publication. Even once it was published, very few copies were produced.

There were originally 20 equations. These were reduced by Heaviside into 8 equations, and these later became the four equations we are familiar with.

==Timeline of Maxwell's Contributions==

'''1885''' - Oliver Heaviside simplifies the Maxwell equations to the ones used today.

'''1897''' - Guglielmo Marcon employs electromagnetic waves for radio communications.

'''1905''' - Albert Einstein uses the Maxwell equations to start his famous theory of special relativity.

'''1920''' - Homes began to use radio to listen to music and voice.

'''1957''' - Sony begins mass producing affordable transistor radios.

'''1973''' - First handheld or cellular mobile telephone networks.

'''2000''' - WiFi expands connectivity of mobile devices to the internet.

[[File:Maxwell3597.jpg]]

== See also ==

[[James Maxwell]]

[[ Maxwell's Equations]]

===Further reading===

The theory itself:

http://www.ymambrini.com/My_World/History_files/maxwell_emf_1865.pdf

==References==

http://www.damtp.cam.ac.uk/user/tong/em/dyson.pdf

http://rsta.royalsocietypublishing.org/content/366/1871/1807

http://silas.psfc.mit.edu/maxwell/

http://www.clerkmaxwellfoundation.org/html/electromagnetic_theory.html

https://www.colorado.edu/physics/phys4510/phys4510_fa05/Chapter1.pdf

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/maxeq2.html#c1

https://www.azooptics.com/Article.aspx?ArticleID=944

[[Category: Theory]]

Maxwell's Electromagnetic Theory

2018-04-17T18:27:51Z

Dsaracino3:

Claimed by Griffin Bonnett Spring 2017. Edited by Danielle Saracino Spring 2018.

Written by Megan Sales. Edited by Grace Newville.

A general description of "A Dynamical Theory of the Electromagnetic Field," proposed by Maxwell in 1865.

==The Main Idea==

"''Light consists in transverse undulations of the same medium which is the cause of electric and magnetic oscillations''" - James Maxwell

In short, Maxwell suggested that light, an electric field, and a magnetic field could all be explained in a single electromagnetic theory. Maxwell’s theory describes that the electric and magnetic fields which were once thought to be two separate fields are actually distinctly different, paired components of the '''same''' field. James Clerk Maxwell developed his theory, with the help of Einstein's prior special relativity theory, that brought together two of the main concepts discussed in this class: electric fields and magnetic fields. These fields have largely been discussed separately, but when Maxwell's Equations were first introduced, the connections became more and more apparent. Maxwell's Electromagnetic Theory brought about the deep relation between electric and magnetic fields, i.e. electromagnetic fields. Maxwell's theory proposed that electric and magnetic fields move as waves at the speed of light. This was the first time electricity, magnetism, and light had been related in such a way. Together, the four equations give a complete description of all of the spatial patters of magnetic and electric fields that are possible anywhere in space for many different varying scenarios.

Brief Overview of Maxwell's Electromagnetic Theory:
https://www.youtube.com/watch?v=50v75xPfhQI

===A Mathematical Model===

Maxwell Equations:

[[File:Maxwell-review.gif]]

These are the four complete Maxwell Equations in their integral form.

1) Gauss's Law relates electric field to the charge enclosed by a "Gaussian Surface." The integral represents the sum of electric flux, so by finding this and multiplying by epsilon-zero, the charge enclosed by the surface may be calculated. The electric flux out of any closed surface is proportional to the total charge enclosed within the surface.

2) Gauss's Law for magnetism states that the sum of magnetic flux for a specific area is equal to zero. This amounts to a statement about the sources of magnetic field. For a magnetic dipole, any closed surface the magnetic flux directed inward toward the south pole will equal the flux outward from the north pole.

3) Faraday's Law directly relates electric and magnetic fields by being able to find the non-Coulomb Electric field that is produced due to a magnetic field and current. The line integral of the electric field around a closed loop is equal to the negative of the rate of change of the magnetic flux through the area enclosed by the loop.

4) Ampere-Maxwell Law is perhaps the most complex of Maxwell's Equations, and involves the derivative of electric flux. In the case of static electric field, the line integral of the magnetic field around a closed loop is proportional to the electric current flowing through the loop.

[[File:Maxwell_equation.jpg]]

[[File:Maxwellunits123.jpg]]

This is the four complete Maxwell Equations in their differential form.

===A Computational Model===

Maxwell's equations can be used to model a multitude of scenarios, but the key idea is that a time-varying magnetic field is associated with an electric field and vice versa. This leads to the concept that by solving the partial differential equations given by these four equations, all fields traveling through space may be modeled, but for most cases the calculations are so complex that they must be done computationally.

Check out [http://www.matterandinteractions.org/student/Mechanics/LectureVideos/Content/Ch23.html this resource] for several interesting demonstrations.

==Examples==

===Gauss's Law Example===

https://www.youtube.com/watch?v=c0S7U6uldsc

===Derivation===

Lengthy, but very informative:

https://www.youtube.com/watch?v=AWI70HXrbG0

==Connectedness==
I first saw Maxwell's Equations in my thermodynamics class last semester. That is what prompted me to explore the theory behind them, as I had only used them in a practical application. That being said, this [https://www.youtube.com/watch?v=UDetOBm9RUs video] shows the derivation of the equations for thermodynamics, something I use as a chemical engineer.

Maxwell's equations also have a direct industrial application. They are used in magnetic machines and to accurately predict electrical machine performance. They also led to the development of the [https://en.wikipedia.org/wiki/Maxwell_stress_tensor Maxwell stress tensor].

==History==

When James Clerk Maxwell came out with his paper, "A dynamical theory of the electromagnetic field," in 1865, it was found hard to understand and widely ignored. Even so, it is one of the most important pieces of theory in our history. He himself downplayed the importance of his theory, putting more emphasis on Kelvin's vortex theory during his own address. Furthermore, it was hard to grasp the concept of intangible fields. Scientists, including Maxwell, tried to picture fields as tangible structures, but to use these mechanical models with the Maxwell equations, they had to be exceedingly complicated. Later, other physicists such as Hertz, Lorentz, and Einstein clarified his theory.

When the paper first was written, it was read to the Royal Society. It was next read and reviewed by many other notable physicists, all prior to its publication. Even once it was published, very few copies were produced.

There were originally 20 equations. These were reduced by Heaviside into 8 equations, and these later became the four equations we are familiar with.

==Timeline of Maxwell's Contributions==

'''1885''' - Oliver Heaviside simplifies the Maxwell equations to the ones used today.

'''1897''' - Guglielmo Marcon employs electromagnetic waves for radio communications.

'''1905''' - Albert Einstein uses the Maxwell equations to start his famous theory of special relativity.

'''1920''' - Homes began to use radio to listen to music and voice.

'''1957''' - Sony begins mass producing affordable transistor radios.

'''1973''' - First handheld or cellular mobile telephone networks.

'''2000''' - WiFi expands connectivity of mobile devices to the internet.

[[File:Maxwell3597.jpg]]

== See also ==

[[James Maxwell]]

[[ Maxwell's Equations]]

===Further reading===

The theory itself:

http://www.ymambrini.com/My_World/History_files/maxwell_emf_1865.pdf

==References==

http://www.damtp.cam.ac.uk/user/tong/em/dyson.pdf

http://rsta.royalsocietypublishing.org/content/366/1871/1807

http://silas.psfc.mit.edu/maxwell/

http://www.clerkmaxwellfoundation.org/html/electromagnetic_theory.html

https://www.colorado.edu/physics/phys4510/phys4510_fa05/Chapter1.pdf

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/maxeq2.html#c1

[[Category: Theory]]

Hooke's Law

2017-04-04T04:26:34Z

Dsaracino3:

This resource page addresses Hooke's Law.

==The Main Idea==

'''Hooke's law''' or the law of elasticity named after 17th century Physicist Robert Hooke is the law that states the Force acting on an elastic object is equal to k*x. In other words, the law states that the force required to stretch an elastic object such as a spring is directly proportional to how far the object stretches. The force may be applied to the spring by stretching, compressing, squeezing, bending, or twisting. The value of k depends on the material, its dimensions, and shape. Hooke's law may also be expressed in terms of stress and strain. Stress is the force applied per unit area of a material and strain is the relative change in shape or size due to a force acting on it.

===A Mathematical Model===

This system can be expressed as F = ks, where k is a constant specific to that material and s is the stretch of the object.
In some cases it will be expressed as F=-ks, in this case F is the restoring force that causes elastic materials to return to their original dimensions rather than the applied force.

===A Computational Model===

[https://trinket.io/glowscript/31d0f9ad9e A vpython visualization of Hooke's Law]

==History==

Hooke's law is named after the 17th century British physicist Robert Hooke. He first stated the law in 1660 as a Latin anagram then published the solution in 1678 named ut tensio, sic vis which translated means "the extension is proportional to the force." Hooke discovered this law when there was a need to navigate trade routes and avoid dangerous waters effectively. He came up with the idea of using a coiled spring in a watch to tell time. Although he wasn't the first to complete the spring based watch, he is credited with the discovery of the relationship of the spring as it is believed to be his idea first.

==Real Life Applications==
In addition to springs, Hooke’s Law also applies in many other situations where an elastic body is deformed. Some examples include inflating a balloon and pulling on a rubber band to measuring the amount of wind force is needed to make a tall building bend and sway. This law has had many real life applications, such as the creation of a balance wheel, the mechanical clock, the portable timepiece, the spring scale and the manometer. Also, because it is a close approximation of all solid bodies, it is applicable to numerous branches of science and engineering. These include the disciplines of seismology, molecular mechanics and acoustics.

==Problem Set==

A few sample problems and their solutions.

===Question 1===
QUESTION:
 What is the force required to stretch a spring whose constant value is 250 N/m by an amount of 0.75 m?

SOLUTION:
 Using the formula F=ks solve the question
 F=force(N)
 k=force constant(N/m)
 s=stretch or compression(m)

F=(250)(0.20)
F=50 N

===Question 2===
QUESTION:
 If 100 N stretches a spring 17 cm, how much stretch can we expect to result from a force of 636 N?

SOLUTION:
 Set up a proportionality statement
 100N/636N=17cm/x
 Solve
 x=108.12cm or 1.0812m

===Question 3===
QUESITON:
 When the weight hung on a spring is increased by 60 N, the new stretch is 15 cm more. If the original stretch is 5 cm, what is the original weight?

SOLUTION:
 [http://www.introduction-to-physics.com/elasticity-problems.html Click Here]

== See also ==

[[Robert Hooke]]
 [[Spring Potential Energy]]
 [[Tension]]
 [[Young's Modulus]]

===Further reading===

[http://hyperphysics.phy-astr.gsu.edu/hbase/permot2.html Elasticity and Hooke's Law]

[http://www.universetoday.com/55027/hookes-law/ What is Hooke's Law? ]

[http://www.britannica.com/science/Hookes-law Encyclopedia Brittanica: Hooke's Law]

===External links===

[https://www.youtube.com/watch?v=dnebaW-a338 Doodle Science provides a brief run through of Hooke's Law.]

[https://www.youtube.com/watch?v=x_0YWeHXZFE An alternate explanation of Hooke's Law with a sample problem set.]

==References==

[http://www.introduction-to-physics.com/elasticity-problems.html]
 [https://www.teachengineering.org/collection/van_/lessons/van_cancer_lesson2/stress_strain_hookes_law_key.pdf]
 [http://hyperphysics.phy-astr.gsu.edu/hbase/permot2.html]
 Invention by Design: How Engineers Get from Thought to Thing. Cambridge, MA: Harvard University Press

[[Category:Contact Interactions]]