Superposition Principle - Revision history

Vpati3 at 03:26, 1 December 2025

2025-12-01T03:26:35Z

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	Applications include medical imaging, antenna array beamforming, engineering simulations, and quantum mechanics applications such as superposing wave functions in schrodinger equation solvers, density functional theory, and quantum chemistry codes.		Applications include medical imaging, antenna array beamforming, engineering simulations, and quantum mechanics applications such as superposing wave functions in schrodinger equation solvers, density functional theory, and quantum chemistry codes.

	[[File:~~Electric_Field_Lines~~.svg\|500px\|center\|Illustration of electric field superposition from multiple point charges]]		[[File:VFPt_charges_plus_minus_thumb.svg.png\|500px\|center\|Illustration of electric field superposition from multiple point charges]]

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-'''Claimed By: Jared Nation'''
+'''Claimed By: Viresh Pati Fall 2025'''
 == The Big Picture ==
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 Conceptually, it is also important to note that an object cannot exert a force on itself, so the sum of all of the forces does not include the object itself.
 ==Examples==

2022-07-24T03:19:35Z

Medium - Three Point Charges and Two Dimensions

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	For this problem, let's consider -q' to be q3, 3q to be q1, and -1 to be q2 and, for the sake of simplicity, we are going to call our constant 'k'		For this problem, let's consider -q' to be q3, 3q to be q1, and -1 to be q2 and, for the sake of simplicity, we are going to call our constant 'k'


	Let's find the forces separately, then add them together:		Let's find the forces separately, then add them together:


	<math> k * (q1q3)/(r)^2 rhat </math>		<math> k * (q1q3)/(r)^2 rhat </math>

	Now that we have the general form of the equation, we plug in variables.		Now that we have the general form of the equation, we plug in variables.


	<math> F1 = k * 3q(-q')/(sqrt(3) * l)^2 * (sin(theta),cos(theta),0) </math>		<math> F1 = k * 3q(-q')/(sqrt(3) * l)^2 * (sin(theta),cos(theta),0) </math>

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Medium - Three Point Charges and Two Dimensions

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 </div>
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 === Medium - Three Point Charges and Two Dimensions===

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Medium - Three Point Charges and Two Dimensions

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	To begin, we recognize that this problem will be using the superposition principle. It is additionally		To begin, we recognize that this problem will be using the superposition principle. It is additionally
	important to recognize that objects can't exert forces on themselves. Keeping ~~these~~ in mind, ~~The~~ force exerted on -q' will be a combination of the forces exerted by 3q and negative q.		important to recognize that objects can't exert forces on themselves. Keeping that in mind, the force exerted on -q' will be a combination of the forces exerted by 3q and negative q.

	For this problem, let's consider -q' to be q3, 3q to be q1, and -1 to be q2 and, ~~For~~ the sake of simplicity, we are going to call our constant 'k'		For this problem, let's consider -q' to be q3, 3q to be q1, and -1 to be q2 and, for the sake of simplicity, we are going to call our constant 'k'


	Let's find the forces separately then add them together:		Let's find the forces separately, then add them together:

2022-07-24T03:12:59Z

Medium - Three Point charges and two Dimensions

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	<math> k* Q^2 * 1/(52d^2) * (2/13 * sqrt(13),-3/13 sqrt(13),0) </math>		<math> k* Q^2 * 1/(52d^2) * (2/13 * sqrt(13),-3/13 sqrt(13),0) </math>

	=== Medium - Three Point ~~charges~~ and ~~two~~ Dimensions===		=== Medium - Three Point Charges and Two Dimensions===
	[[File:Superpos file.JPG]]		[[File:Superpos file.JPG]]

2022-07-24T03:12:03Z

Medium - Three Point charges and two Dimensions

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	</div>		</div>

	=== Medium - Three Point ~~charges~~ and ~~two~~ Dimensions ===		=== Medium - Three Point Charges and Two Dimensions ===
	[[File:Superposfile2.JPG]]		[[File:Superposfile2.JPG]]

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	<math> k* Q^2 * 1/(52d^2) * (2/13 * sqrt(13),-3/13 sqrt(13),0) </math>		<math> k* Q^2 * 1/(52d^2) * (2/13 * sqrt(13),-3/13 sqrt(13),0) </math>



	=== Medium - Three Point charges and two Dimensions===		=== Medium - Three Point charges and two Dimensions===

2022-07-24T03:11:36Z

Examples

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	<math>\vec{E_2} = \frac{1}{4 \pi \epsilon_0}\frac{q_2}{r_2^2}\hat{r_2} = (9e9)\frac{1e-5C}{1m^2}(-1m) = -9e4\frac{N}{C}</math>		<math>\vec{E_2} = \frac{1}{4 \pi \epsilon_0}\frac{q_2}{r_2^2}\hat{r_2} = (9e9)\frac{1e-5C}{1m^2}(-1m) = -9e4\frac{N}{C}</math>

	By this point, you have the individual contributions of each charge. To get the net contribution of all the charges, you only need to add them.		At this point, you have the individual contributions of each charge. To get the net contribution of all the charges, you only need to add them.

	<math>\vec{E_1}+\vec{E_2}=9e5\frac{N}{C}-9e4\frac{N}{C}= 8.1e5\frac{N}{C}</math>		<math>\vec{E_1}+\vec{E_2}=9e5\frac{N}{C}-9e4\frac{N}{C}= 8.1e5\frac{N}{C}</math>

2022-07-24T03:10:51Z

Simple - Two Point Charges and One Dimension

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	<math>\vec{E_1} = \frac{1}{4 \pi \epsilon_0}\frac{q_1}{r_1^2}\hat{r_1} = (9e9)\frac{1e-4C}{1m^2}(1m) = 9e5\frac{N}{C}</math>		<math>\vec{E_1} = \frac{1}{4 \pi \epsilon_0}\frac{q_1}{r_1^2}\hat{r_1} = (9e9)\frac{1e-4C}{1m^2}(1m) = 9e5\frac{N}{C}</math>

	<math>\vec{E_2} = \frac{1}{4 \pi \epsilon_0}\frac{q_2}{r_2^2}\hat{r_2} = (9e9)\frac{1e-5C}{1m^2}(-1m) = -9e4\frac{N}{C}</math>		<math>\vec{E_2} = \frac{1}{4 \pi \epsilon_0}\frac{q_2}{r_2^2}\hat{r_2} = (9e9)\frac{1e-5C}{1m^2}(-1m) = -9e4\frac{N}{C}</math>

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	</div>		</div>
	</div>		</div>

	=== Medium - Three Point charges and two Dimensions ===		=== Medium - Three Point charges and two Dimensions ===
	[[File:Superposfile2.JPG]]		[[File:Superposfile2.JPG]]

2022-07-24T03:09:29Z

A Mathematical Model

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	<math>\hat{r_i}</math> is the vector pointing from the particle to the observation location.		<math>\hat{r_i}</math> is the vector pointing from the particle to the observation location.

	Conceptually is is also important to note that an object cannot exert a force on itself, so the sum of all of the forces does not include the object itself.		Conceptually, it is also important to note that an object cannot exert a force on itself, so the sum of all of the forces does not include the object itself.

	==Examples==		==Examples==