Maxwell's Electromagnetic Theory - Revision history

Dkim3019 at 03:31, 24 November 2025

2025-11-24T03:31:13Z

← Older revision		Revision as of 23:31, 23 November 2025
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	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 patterns of magnetic and electric fields that are possible anywhere in space for many different varying scenarios. In addition, Maxwell recognized that the originally written Ampere's Law was incomplete. He introduced the idea of displacement current, which accounts for changing electric fields even in regions where no physical charges are flowing. This new idea ensured that the equations obeyed conservation of charge. Without this change, electromagnetic waves would not mathematically emerge from the theory at all.		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 patterns of magnetic and electric fields that are possible anywhere in space for many different varying scenarios. In addition, Maxwell recognized that the originally written Ampere's Law was incomplete. He introduced the idea of displacement current, which accounts for changing electric fields even in regions where no physical charges are flowing. This new idea ensured that the equations obeyed conservation of charge. Without this change, electromagnetic waves would not mathematically emerge from the theory at all.

			'''How Maxwell’s Equations Predict Electromagnetic Waves'''

			One of Maxwell’s most important accomplishment was showing that his four equations naturally lead to the existence of self-propagating electromagnetic waves. This connection is often mentioned in lecture but not shown explicitly. The key idea is that a changing electric field creates a magnetic field, and a changing magnetic field creates an electric field, forming a “loop” that can travel through space on its own. This was the first theoretical prediction that light is an electromagnetic wave.

	Brief Overview of Maxwell's Electromagnetic Theory:		Brief Overview of Maxwell's Electromagnetic Theory:

Dkim3019 at 03:16, 24 November 2025

2025-11-24T03:16:00Z

← Older revision		Revision as of 23:16, 23 November 2025
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	The direction of the current in the coil is counter-clockwise. This is because the direction of dB/dt is into the page, which is determined by pointing your thumb in the direction of I and curling your fingers to find B, and then using the fact that the wire is moving towards the loop to determine that it is growing larger over time. In order to counter-act this, the current produced in the coil will make a magnetic field out of the page. By applying right-hand rule again, you can determine that the current must go counter-clockwise to do this.		The direction of the current in the coil is counter-clockwise. This is because the direction of dB/dt is into the page, which is determined by pointing your thumb in the direction of I and curling your fingers to find B, and then using the fact that the wire is moving towards the loop to determine that it is growing larger over time. In order to counter-act this, the current produced in the coil will make a magnetic field out of the page. By applying right-hand rule again, you can determine that the current must go counter-clockwise to do this.


			===Maxwell's 4th Equation (Displacement Current)===

			'''Problem'''

			A parallel-plate capacitor is being charged. The plate area is A = 0.020 m^2, the electric field between the plates is increasing at a rate of 1.5 × 10^6 V/m, and the separation between the plates is 1.0 mm.

			'''Solution'''

			[[File:maxwell1.jpeg]]

			Created by Dana Kim, a Georgia Tech Student

	===Gauss's Law Example===		===Gauss's Law Example===

Dkim3019 at 02:36, 16 November 2025

2025-11-16T02:36:23Z

← Older revision		Revision as of 22:36, 15 November 2025
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	"''Light consists in transverse undulations of the same medium which is the cause of electric and magnetic oscillations''" - James Maxwell		"''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 patterns of magnetic and electric fields that are possible anywhere in space for many different varying scenarios.		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 patterns of magnetic and electric fields that are possible anywhere in space for many different varying scenarios. In addition, Maxwell recognized that the originally written Ampere's Law was incomplete. He introduced the idea of displacement current, which accounts for changing electric fields even in regions where no physical charges are flowing. This new idea ensured that the equations obeyed conservation of charge. Without this change, electromagnetic waves would not mathematically emerge from the theory at all.

	Brief Overview of Maxwell's Electromagnetic Theory:		Brief Overview of Maxwell's Electromagnetic Theory:
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	Matters and Interactions: 4th Edition		Matters and Interactions: 4th Edition

			https://www.khanacademy.org/science/in-in-class-12th-physics-india/in-in-electromagnetic-waves/x51bd77206da864f3:displacement-current/v/displacement-current-ampere-maxwell-s-law

	[[Category: Theory]]		[[Category: Theory]]

Dkim3019 at 02:26, 16 November 2025

2025-11-16T02:26:45Z

← Older revision		Revision as of 22:26, 15 November 2025
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	~~Claimed by Griffin Bonnett Spring 2017. Edited by Danielle Saracino Spring 2018. Claimed by Braeden Collins Fall 2018.~~'''Claimed by ~~Carissa Lucas~~ Fall ~~2023.~~'''		'''Claimed by Dana Kim Fall 2025'''

	Written by Megan Sales. Edited by Grace Newville.		Written by Megan Sales. Edited by Grace Newville.

Clucas49 at 09:35, 27 November 2023

2023-11-27T09:35:26Z

← Older revision		Revision as of 05:35, 27 November 2023
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	Written by Megan Sales. Edited by Grace Newville.		Written by Megan Sales. Edited by Grace Newville.

	~~<iframe src="https://trinket.io/embed/glowscript/fa14ed42b6" width="100%" height="356" frameborder="0" marginwidth="0" marginheight="0" allowfullscreen></iframe>~~

	~~[embed\|https://trinket.io/glowscript/fa14ed42b6?toggleCode=true]~~

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

			Here is a model of the electric and magnetic waves that are described in Maxwell's theory, note that they are perpendicular to each other and oscillate together. Source Code: https://trinket.io/glowscript/fa14ed42b6?toggleCode=true (Made by Carissa Lucas, a Georgia Tech Student)

			[[File:EM Waves.jpg]]

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

Clucas49 at 09:29, 27 November 2023

2023-11-27T09:29:00Z

← Older revision		Revision as of 05:29, 27 November 2023
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	Written by Megan Sales. Edited by Grace Newville.		Written by Megan Sales. Edited by Grace Newville.

			<iframe src="https://trinket.io/embed/glowscript/fa14ed42b6" width="100%" height="356" frameborder="0" marginwidth="0" marginheight="0" allowfullscreen></iframe>

			[embed\|https://trinket.io/glowscript/fa14ed42b6?toggleCode=true]

	A general description of "A Dynamical Theory of the Electromagnetic Field," proposed by Maxwell in 1865.		A general description of "A Dynamical Theory of the Electromagnetic Field," proposed by Maxwell in 1865.
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	https://opentextbc.ca/physicstestbook2/chapter/maxwells-equations-electromagnetic-waves-predicted-and-observed/		https://opentextbc.ca/physicstestbook2/chapter/maxwells-equations-electromagnetic-waves-predicted-and-observed/

			https://www.msuperl.org/wp/icsam/computational-activities/electromagnetic-investigation/

	Matters and Interactions: 4th Edition		Matters and Interactions: 4th Edition

	[[Category: Theory]]		[[Category: Theory]]

Clucas49 at 08:47, 27 November 2023

2023-11-27T08:47:08Z

← Older revision		Revision as of 04:47, 27 November 2023
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	[[File:Maxwell1.jpg\|400px]]		[[File:Maxwell1.jpg\|400px]]

			Creater by Braeden Collins, a Georgia Tech Student

	===Maxwell's 2nd Equation (Gauss's Law for Magnetic Fields)===		===Maxwell's 2nd Equation (Gauss's Law for Magnetic Fields)===
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	[[File:Maxwell2.jpg\|400px]]		[[File:Maxwell2.jpg\|400px]]

			Created by Braeden Collins, a Georgia Tech Student

	===Maxwell's 3rd Equation (Faraday's Law)===		===Maxwell's 3rd Equation (Faraday's Law)===
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	[[File:Maxwell3corrected.jpg\|400px]]		[[File:Maxwell3corrected.jpg\|400px]]

			Created by Braeden Collins, a Georgia Tech Student

	The direction of the current in the coil is counter-clockwise. This is because the direction of dB/dt is into the page, which is determined by pointing your thumb in the direction of I and curling your fingers to find B, and then using the fact that the wire is moving towards the loop to determine that it is growing larger over time. In order to counter-act this, the current produced in the coil will make a magnetic field out of the page. By applying right-hand rule again, you can determine that the current must go counter-clockwise to do this.		The direction of the current in the coil is counter-clockwise. This is because the direction of dB/dt is into the page, which is determined by pointing your thumb in the direction of I and curling your fingers to find B, and then using the fact that the wire is moving towards the loop to determine that it is growing larger over time. In order to counter-act this, the current produced in the coil will make a magnetic field out of the page. By applying right-hand rule again, you can determine that the current must go counter-clockwise to do this.

Clucas49 at 08:37, 27 November 2023

2023-11-27T08:37:14Z

← Older revision		Revision as of 04:37, 27 November 2023
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	==The Main Idea==		==The Main Idea==
			[[File:Electromagnetic wave EN.svg.png]]

			Source: https://commons.wikimedia.org/wiki/File:Electromagnetic_wave_EN.svg (Used through Creative Commons License)

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

Clucas49 at 08:24, 27 November 2023

2023-11-27T08:24:39Z

← Older revision		Revision as of 04:24, 27 November 2023
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	Maxwell Equations:		Maxwell Equations:

	[[File:Maxwell~~-review~~.~~gif~~]]		[[File:Maxwell Equations Integral Form.jpg]]

	These are the four complete Maxwell Equations in their integral form.		These are the four complete Maxwell Equations in their integral form.
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	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.		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:Maxwell Equations Differential Form.jpg]]

	~~[[File:Maxwellunits123~~.jpg]]

	These are the four complete Maxwell Equations in their differential form.		These are the four complete Maxwell Equations in their differential form.
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	===Maxwell's 1st Equation (Gauss's Law for Electric Fields)===		===Maxwell's 1st Equation (Gauss's Law for Electric Fields)===

	[[File:Maxwell~~'s1st~~.jpg]]		[[File:Maxwell Equation 1.jpg]]

	'''Problem'''		'''Problem'''
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	===Maxwell's 2nd Equation (Gauss's Law for Magnetic Fields)===		===Maxwell's 2nd Equation (Gauss's Law for Magnetic Fields)===

	[[File:Maxwell~~'s2nd~~.jpg]]		[[File:Maxwell Equation 2.jpg]]

	'''Problem'''		'''Problem'''
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	===Maxwell's 3rd Equation (Faraday's Law)===		===Maxwell's 3rd Equation (Faraday's Law)===

	[[File:Maxwell~~'s3rd~~.jpg]]		[[File:Maxwell Equation 3.jpg]]

	'''Problem'''		'''Problem'''
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	The discovery of electromagnetic radiation led to the development of radio and infra-red telescopes, currently exploring the farthest reaches of space.		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~~]]		[[File:Maxwell's Theory Applications.png]]

	== See also ==		== See also ==

Clucas49 at 07:02, 27 November 2023

2023-11-27T07:02:10Z

← Older revision		Revision as of 03:02, 27 November 2023
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	Maxwell’s theory proved that electric and magnetic forces are not separate, 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.		Maxwell’s theory proved that electric and magnetic forces are not separate, 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.		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.		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.