Inductors - Revision history

Ebarden3: Edited by Ella Barden Spring 2026

2026-04-27T03:48:45Z

Edited by Ella Barden Spring 2026

← Older revision		Revision as of 23:48, 26 April 2026
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			Page Claimed by Ella Barden Spring 2026
	~~Short Description of Inductors~~
	~~'''Rohan Mundkur (Fall 2016)'''~~

	==Inductors - Conceptual Overview==		==Inductors - Conceptual Overview==
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	The conductor that makes up the inductor will have a current running through it, and as this non-changing current runs, a magnetic field will be created within the center of the coil. Therefore, as the current begins to change, the respective flux through a ring of the coil will change as well. As we know, the ratio of a change in flux to the respective change in time will provide us with the potential difference resulting from the change in current. By multiplying this potential difference by the number of loops in the circuit, we are able to obtain the coil's overall potential difference due to the single change in current.		The conductor that makes up the inductor will have a current running through it, and as this non-changing current runs, a magnetic field will be created within the center of the coil. Therefore, as the current begins to change, the respective flux through a ring of the coil will change as well. As we know, the ratio of a change in flux to the respective change in time will provide us with the potential difference resulting from the change in current. By multiplying this potential difference by the number of loops in the circuit, we are able to obtain the coil's overall potential difference due to the single change in current.

			This phenomenon is tied to the concept of magnetic energy storage. Unlike a capacitor that stores energy in an electric field between plates, an inductor stores energy within its magnetic field. When the current flows, the magnetic field builds up, and when the current attempts to drop, that stored magnetic energy is released back into the circuit to keep the electrons moving.

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	The essential directional behavior of the induced emf is to be opposite the coil's magnetic field when the current increases and in line with the coil's magnetic field when the current decreases. We can make this assumption because if the behaviors were reversed, any change in current would result in an infinite increase or decrease. This phenomenon occurs because of the direction of the non-Coulomb (NC) electric field's direction in relation to the Coulomb electric field's direction (direction of current). When the current through the inductor increases, the NC electric field curls in the opposite direction of the current, but when the current through the inductor decreases, the NC electric field curls in the same direction as the current.		The essential directional behavior of the induced emf is to be opposite the coil's magnetic field when the current increases and in line with the coil's magnetic field when the current decreases. We can make this assumption because if the behaviors were reversed, any change in current would result in an infinite increase or decrease. This phenomenon occurs because of the direction of the non-Coulomb (NC) electric field's direction in relation to the Coulomb electric field's direction (direction of current). When the current through the inductor increases, the NC electric field curls in the opposite direction of the current, but when the current through the inductor decreases, the NC electric field curls in the same direction as the current.

			This is fundamentally an expression of Lenz’s Law, which states that the direction of an induced current is such that it creates a magnetic field opposing the change in the original magnetic flux. You can think of it as a form of electrical inertia. Just as a heavy object resists a change in its state of motion, an inductor resists a change in the state of the current flowing through it.

	The mathematical characterization of this phenomenon will be described in greater detail below.		The mathematical characterization of this phenomenon will be described in greater detail below.
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	The derivation below begins by providing the formula for the magnetic field within a solenoid and continues by applying this magnetic field (and subsequent changes due to change in current) to the equation for flux given the solenoid is comprised of "N" rings with radius "R". After determining the emf of a single loop, we multiply by "N" to obtain the emf of the entire solenoid. Finally, in order to simplify our expression and provide a segway to the exploration of non-solenoid inductor shapes, we represent the proportion of total emf to change in current by the variable "L" whose units are henries (H).		The derivation below begins by providing the formula for the magnetic field within a solenoid and continues by applying this magnetic field (and subsequent changes due to change in current) to the equation for flux given the solenoid is comprised of "N" rings with radius "R". After determining the emf of a single loop, we multiply by "N" to obtain the emf of the entire solenoid. Finally, in order to simplify our expression and provide a segway to the exploration of non-solenoid inductor shapes, we represent the proportion of total emf to change in current by the variable "L" whose units are henries (H).

			The value of L is determined by the physical geometry of the component. For a standard solenoid, the inductance is calculated by the permeability of free space multiplied by the square of the number of turns, the cross sectional area, and then divided by the length of the solenoid. This highlights why adding a high permeability core, such as iron, inside the coil significantly boosts the inductance because it concentrates the magnetic flux.

	[[File:Screen_Shot_2016-11-27_at_9.52.28_PM.png]]		[[File:Screen_Shot_2016-11-27_at_9.52.28_PM.png]]
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	[[File:physics gif 1.gif]]		[[File:physics gif 1.gif]]

	Note, inductance and resistance have inverse effects on current.		Note, inductance and resistance have inverse effects on current. Resistance dissipates energy as heat while inductance stores it temporarily. This relationship is often characterized in RL circuits by a time constant, which is the ratio of inductance to resistance. This constant tells us how quickly the current will reach its maximum value after a switch is closed.

	[[File:physics gif 2.gif]]		[[File:physics gif 2.gif]]
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	==Examples==		==Examples==


	===Simple===		===Simple===
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	An infinite straight wire with current I is next to a solenoid of 10 square loops with dimensions L. The side of the solenoid closest to the wire is at a distance "s".		An infinite straight wire with current I is next to a solenoid of 10 square loops with dimensions L. The side of the solenoid closest to the wire is at a distance "s".

			This problem requires us to integrate the magnetic field of the infinite wire over the area of the square loops. Since the magnetic field of a wire decreases as the inverse of the distance, the flux is not uniform across the square loops. We would set up an integral from s to s plus L to find the total flux through one loop and then multiply by the number of turns.

	[[File:Screen_Shot_2016-11-27_at_11.27.25_PM.png]]		[[File:Screen_Shot_2016-11-27_at_11.27.25_PM.png]]
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	''How is this topic connected to something that you are interested in?''		''How is this topic connected to something that you are interested in?''

	I find the concept of inductance incredibly interesting because it serves as an almost natural buffer to any deviation from "equilibrium". This intrigues me because I find biology and chemistry very interesting, and within those two subjects, we often discuss homeostasis and chemical equilibrium and the natural buffers that exist in order to counteract movements away from the state of equilibrium.		I find the concept of inductance incredibly interesting because it serves as an almost natural buffer to any deviation from "equilibrium". This intrigues me because I find biology and chemistry very interesting, and within those two subjects, we often discuss homeostasis and chemical equilibrium and the natural buffers that exist in order to counteract movements away from the state of equilibrium. It is fascinating how the laws of physics provide a mechanism to maintain stability in a system just like biological systems maintain a constant internal environment.

	''Is there an interesting industrial application?''		''Is there an interesting industrial application?''

	Inductors have a vast range of industrial applications ranging from transformers that help manage the power supply to massive cities or energy storage for personal computers. The defining characteristics of inductors also enable them to be used at traffic lights in order to gauge traffic flow at intersections. Living in Atlanta, we all know the horrors of rush hour, so I find this industrial application incredibly interesting.		Inductors have a vast range of industrial applications ranging from transformers that help manage the power supply to massive cities or energy storage for personal computers. The defining characteristics of inductors also enable them to be used at traffic lights in order to gauge traffic flow at intersections. Living in Atlanta, we all know the horrors of rush hour, so I find this industrial application incredibly interesting. These sensors work as inductive loops buried in the road. When a large metal object like a car sits on top of them, the inductance of the loop changes, which signals the computer to change the light.

	For more information on how inductors play a role in traffic control, please visit this link from HowStuffWorks: http://auto.howstuffworks.com/car-driving-safety/safety-regulatory-devices/question234.htm		For more information on how inductors play a role in traffic control, please visit this link from HowStuffWorks: http://auto.howstuffworks.com/car-driving-safety/safety-regulatory-devices/question234.htm
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	''How is it connected to your major?''		''How is it connected to your major?''

	The concept of inductors does not directly relate to my major as I am a Business major. However, I am taking Pre-Medical Courses, and as mentioned earlier in this section, the way in which inductors provide a natural buffer within circuits is mirrored through various biology and chemistry concepts.		The concept of inductors does not directly relate to my major as I am a Business major. However, I am taking Pre-Medical Courses, and as mentioned earlier in this section, the way in which inductors provide a natural buffer within circuits is mirrored through various biology and chemistry concepts. For example, in the human body, the pH of our blood is kept stable by buffer systems that resist change, much like an inductor resists a change in current.

	==History==		==History==
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	Joseph Henry is the father of inductance. Although Joseph Henry's work on self-inductance may not hold the same place in common knowledge as Sir Isaac Newton's Laws, Henry had an enormous impact on history during the 19th century. The American scientist discovered self-inductance when performing experiments with electromagnets, and although much credit for this work is given to the Englishman Michael Faraday, who published his work first, many suggest that Henry discovered these concepts first. Because of Henry's importance in this field, the units of inductance take his name: henry (H).		Joseph Henry is the father of inductance. Although Joseph Henry's work on self-inductance may not hold the same place in common knowledge as Sir Isaac Newton's Laws, Henry had an enormous impact on history during the 19th century. The American scientist discovered self-inductance when performing experiments with electromagnets, and although much credit for this work is given to the Englishman Michael Faraday, who published his work first, many suggest that Henry discovered these concepts first. Because of Henry's importance in this field, the units of inductance take his name: henry (H).

	Henry also greatly impacted scientific advancement within America as he was the first Smithsonian Secretary.		Henry also greatly impacted scientific advancement within America as he was the first Smithsonian Secretary. His dedication to the dissemination of knowledge helped establish a foundation for American research that persists today.

	The discovery of inductors quickly led to the discovery of something super cool: transformers. The simplest version of a transformer is just two inductors next to each other not touching because the magnetic field of each inductor affects the other. This discovery kicked off years of experimentation. Eventually, William Stanley of George Westinghouse created the first commercially viable transformer in the 1880s. This launched George Westinghouse into the public consciousness and they quickly became a worldwide infrastructure powerhouse--even powering the World’s Columbian Exposition in Chicago in 1893.		The discovery of inductors quickly led to the discovery of something super cool: transformers. The simplest version of a transformer is just two inductors next to each other not touching because the magnetic field of each inductor affects the other. This discovery kicked off years of experimentation. Eventually, William Stanley of George Westinghouse created the first commercially viable transformer in the 1880s. This launched George Westinghouse into the public consciousness and they quickly became a worldwide infrastructure powerhouse--even powering the World’s Columbian Exposition in Chicago in 1893.

			This period was known as the War of Currents, where Westinghouse’s alternating current (AC) system, which relied heavily on transformers and inductors, eventually triumphed over Thomas Edison’s direct current (DC) system for long distance power transmission.

	In a greater, historical perspective, the introduction of inductors into complex circuits provided the basis for the evolution of modern power grids and electric technology as we know it today. The supply of the massive amounts of electricity that today's society consumes would be incredibly unstable without transformers, whose properties are made possible by inductors.		In a greater, historical perspective, the introduction of inductors into complex circuits provided the basis for the evolution of modern power grids and electric technology as we know it today. The supply of the massive amounts of electricity that today's society consumes would be incredibly unstable without transformers, whose properties are made possible by inductors.

Smiley: /* History */

2017-12-04T01:01:19Z

History

← Older revision		Revision as of 21:01, 3 December 2017
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	Henry also greatly impacted scientific advancement within America as he was the first Smithsonian Secretary.		Henry also greatly impacted scientific advancement within America as he was the first Smithsonian Secretary.

			The discovery of inductors quickly led to the discovery of something super cool: transformers. The simplest version of a transformer is just two inductors next to each other not touching because the magnetic field of each inductor affects the other. This discovery kicked off years of experimentation. Eventually, William Stanley of George Westinghouse created the first commercially viable transformer in the 1880s. This launched George Westinghouse into the public consciousness and they quickly became a worldwide infrastructure powerhouse--even powering the World’s Columbian Exposition in Chicago in 1893.

	In a greater, historical perspective, the introduction of inductors into complex circuits provided the basis for the evolution of modern power grids and electric technology as we know it today. The supply of the massive amounts of electricity that today's society consumes would be incredibly unstable without transformers, whose properties are made possible by inductors.		In a greater, historical perspective, the introduction of inductors into complex circuits provided the basis for the evolution of modern power grids and electric technology as we know it today. The supply of the massive amounts of electricity that today's society consumes would be incredibly unstable without transformers, whose properties are made possible by inductors.

Smiley at 00:47, 4 December 2017

2017-12-04T00:47:24Z

← Older revision		Revision as of 20:47, 3 December 2017
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	http://siarchives.si.edu/history/joseph-henry		http://siarchives.si.edu/history/joseph-henry

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

Smiley: /* Computational Model */

2017-12-04T00:43:33Z

Computational Model

← Older revision		Revision as of 20:43, 3 December 2017
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	[[File:physics gif 2.gif]]		[[File:physics gif 2.gif]]

	Here's one final gif to ~~drive~~ the ~~concept home~~		Here's one final gif to show how inductors are crucial in the design of power supplies. See how the force is created?

	[[File:physics gif 3.gif]]		[[File:physics gif 3.gif]]
	(original simulation ~~as seen in gifs was~~ created by ~~Physics Videos youtube channel~~)
			(original simulation created by Eugene Khutoryansky on Youtube)

	==Examples==		==Examples==

Smiley: /* Computational Model */

2017-12-04T00:41:06Z

Computational Model

← Older revision		Revision as of 20:41, 3 December 2017
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	===Computational Model===		===Computational Model===
	The following sequence is a visualization of inductors in a simple circuit		The following sequence is a visualization of inductors in a simple circuit

	[[File:physics gif 1.gif]]		[[File:physics gif 1.gif]]

	Note, inductance and resistance have inverse effects on current.		Note, inductance and resistance have inverse effects on current.

	[[File:physics gif 2.gif]]		[[File:physics gif 2.gif]]

	Here's one final gif to drive the concept home		Here's one final gif to drive the concept home

	[[File:physics gif 3.gif]]		[[File:physics gif 3.gif]]
			(original simulation as seen in gifs was created by Physics Videos youtube channel)

	==Examples==		==Examples==

Smiley: these are allowed under the fair use act due to significant modification

2017-11-30T04:53:30Z

these are allowed under the fair use act due to significant modification

← Older revision		Revision as of 00:53, 30 November 2017
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	The derivation below begins by providing the formula for the magnetic field within a solenoid and continues by applying this magnetic field (and subsequent changes due to change in current) to the equation for flux given the solenoid is comprised of "N" rings with radius "R". After determining the emf of a single loop, we multiply by "N" to obtain the emf of the entire solenoid. Finally, in order to simplify our expression and provide a segway to the exploration of non-solenoid inductor shapes, we represent the proportion of total emf to change in current by the variable "L" whose units are henries (H).		The derivation below begins by providing the formula for the magnetic field within a solenoid and continues by applying this magnetic field (and subsequent changes due to change in current) to the equation for flux given the solenoid is comprised of "N" rings with radius "R". After determining the emf of a single loop, we multiply by "N" to obtain the emf of the entire solenoid. Finally, in order to simplify our expression and provide a segway to the exploration of non-solenoid inductor shapes, we represent the proportion of total emf to change in current by the variable "L" whose units are henries (H).

	[[File:Screen_Shot_2016-11-27_at_9.52.28_PM.png~~]][[File:physics gif 2.gif~~]]		[[File:Screen_Shot_2016-11-27_at_9.52.28_PM.png]]

	===Computational Model===		===Computational Model===

Smiley: /* Computational Model */

2017-11-30T04:50:58Z

Computational Model

← Older revision		Revision as of 00:50, 30 November 2017
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	The following sequence is a visualization of inductors in a simple circuit		The following sequence is a visualization of inductors in a simple circuit
	[[File:physics gif 1.gif]]		[[File:physics gif 1.gif]]

	Note, inductance and resistance have inverse effects on current.		Note, inductance and resistance have inverse effects on current.
	[[File:physics gif 2.gif]]		[[File:physics gif 2.gif]]

	Here's one final gif to drive the concept home		Here's one final gif to drive the concept home
	[[File:physics gif 3.gif]]		[[File:physics gif 3.gif]]

Smiley at 04:47, 30 November 2017

2017-11-30T04:47:19Z

← Older revision		Revision as of 00:47, 30 November 2017
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	The derivation below begins by providing the formula for the magnetic field within a solenoid and continues by applying this magnetic field (and subsequent changes due to change in current) to the equation for flux given the solenoid is comprised of "N" rings with radius "R". After determining the emf of a single loop, we multiply by "N" to obtain the emf of the entire solenoid. Finally, in order to simplify our expression and provide a segway to the exploration of non-solenoid inductor shapes, we represent the proportion of total emf to change in current by the variable "L" whose units are henries (H).		The derivation below begins by providing the formula for the magnetic field within a solenoid and continues by applying this magnetic field (and subsequent changes due to change in current) to the equation for flux given the solenoid is comprised of "N" rings with radius "R". After determining the emf of a single loop, we multiply by "N" to obtain the emf of the entire solenoid. Finally, in order to simplify our expression and provide a segway to the exploration of non-solenoid inductor shapes, we represent the proportion of total emf to change in current by the variable "L" whose units are henries (H).

	[[File:Screen_Shot_2016-11-27_at_9.52.28_PM.png]]		[[File:Screen_Shot_2016-11-27_at_9.52.28_PM.png]][[File:physics gif 2.gif]]

			===Computational Model===
			The following sequence is a visualization of inductors in a simple circuit
			[[File:physics gif 1.gif]]
			Note, inductance and resistance have inverse effects on current.
			[[File:physics gif 2.gif]]
			Here's one final gif to drive the concept home
			[[File:physics gif 3.gif]]

	==Examples==		==Examples==

Rmundkur3: /* Difficult */

2016-11-28T04:28:17Z

Difficult

← Older revision		Revision as of 00:28, 28 November 2016
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	An infinite straight wire with current I is next to a solenoid of 10 square loops with dimensions L. The side of the solenoid closest to the wire is at a distance "s".		An infinite straight wire with current I is next to a solenoid of 10 square loops with dimensions L. The side of the solenoid closest to the wire is at a distance "s".

	[[File:~~Inductancehard1~~.~~png]]~~		[[File:Screen_Shot_2016-11-27_at_11.27.25_PM.png]]
	~~[[File:Inductancehard2~~.png]]

	==Connectedness==		==Connectedness==

Rmundkur3: /* Difficult */

2016-11-28T04:12:15Z

Difficult

← Older revision		Revision as of 00:12, 28 November 2016
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	===Difficult===		===Difficult===

	~~This problem~~ is ~~taken from this website: http://www~~.~~physics.umd.edu/~~		An infinite straight wire with current I is next to a solenoid of 10 square loops with dimensions L. The side of the solenoid closest to the wire is at a distance "s".
	~~However, it~~ is a ~~great problem that delves into the difficulty of solving induced emf problems, since it can be more than just plugging in variables~~.

	[[File:Inductancehard1.png]]		[[File:Inductancehard1.png]]