Superposition principle - Revision history

Rsharma443: /* The Main Idea */

2025-12-01T04:26:39Z

The Main Idea

← Older revision		Revision as of 00:26, 1 December 2025
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	The superposition principle says that when several influences act on a system, the total response is the sum of the individual responses. For electric fields, this means each charge creates its own field independently, and the net field is found by adding all of them as vectors.		The superposition principle says that when several influences act on a system, the total response is the sum of the individual responses. For electric fields, this means each charge creates its own field independently, and the net field is found by adding all of them as vectors.

	~~The superposition principle~~ shows up in many areas of physics and engineering. In circuits, the total voltage at a node can be found by adding contributions from multiple sources. In mechanics, forces from different components of a structure add to give a net reaction. In fields, superposition makes it possible to calculate complex electric and magnetic environments by breaking the problem into simpler pieces.		It shows up in many areas of physics and engineering. In circuits, the total voltage at a node can be found by adding contributions from multiple sources. In mechanics, forces from different components of a structure add to give a net reaction. In fields, superposition makes it possible to calculate complex electric and magnetic environments by breaking the problem into simpler pieces.

	~~The~~ key idea is that each contribution acts independently. Nothing “distorts” another field, so the total is just the vector addition of all of them.		All in all, the key idea is that each contribution acts independently. Nothing “distorts” another field, so the total is just the vector addition of all of them.

	===A Mathematical Model===		===A Mathematical Model===
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	Notice that this uses the principle of superposition. The magnetic and electric fields of the two particles in the dipole are added. This determines the net field at the observation location and is therefore a perfect example of superposition. This is a very elegant and simple example of the principle. It is essentially stated here as the net force as the sum of all other forces. When using the principle in this way it is very important to note the direction of the forces, as they greatly effect the outcome of the answer.		Notice that this uses the principle of superposition. The magnetic and electric fields of the two particles in the dipole are added. This determines the net field at the observation location and is therefore a perfect example of superposition. This is a very elegant and simple example of the principle. It is essentially stated here as the net force as the sum of all other forces. When using the principle in this way it is very important to note the direction of the forces, as they greatly effect the outcome of the answer.

	==Examples==		==Examples==

Rsharma443: improved main idea, made changes to glowscript and equations, removed redundancy and irrelevant information like "better major like me" jokes

2025-12-01T04:25:33Z

improved main idea, made changes to glowscript and equations, removed redundancy and irrelevant information like "better major like me" jokes

← Older revision		Revision as of 00:25, 1 December 2025
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	'''Claimed by ~~Ryan Yeung: April 8, 2017~~'''		'''Claimed by Rithwik Sharma Fall 2025'''

	This ~~topic covers~~ the ~~Superposition Principle. This was the first~~ and ~~original article on this topic (also the best). However it's now being edited~~, and ~~therefore has become ever better than~~ the ~~best~~.		This page explains the superposition principle and brings together examples, models, and applications to make the idea easier to learn.

	==The Main Idea==		==The Main Idea==

	The superposition principle ~~essentially states~~ that in a ~~given closed~~ system, the ~~'reaction' of an object to outside forces~~ is the sum of the ~~outside force acting on it~~. ~~These forces can act along multiple dimensions~~, ~~therefore meaning that vector notation will be needed~~. ~~More simply stated the~~ principle ~~states that~~ the ~~sum~~ of a ~~systems responses is the same as the~~ net ~~result of the forces taken as individuals~~. In ~~order for the~~ superposition ~~principle~~ to ~~apply~~, the ~~system must be linear. This means~~ the ~~reaction~~ of ~~the system follows a linear predictable pattern~~.		The superposition principle says that when several influences act on a system, the total response is the sum of the individual responses. For electric fields, this means each charge creates its own field independently, and the net field is found by adding all of them as vectors.

			The superposition principle shows up in many areas of physics and engineering. In circuits, the total voltage at a node can be found by adding contributions from multiple sources. In mechanics, forces from different components of a structure add to give a net reaction. In fields, superposition makes it possible to calculate complex electric and magnetic environments by breaking the problem into simpler pieces.

			The key idea is that each contribution acts independently. Nothing “distorts” another field, so the total is just the vector addition of all of them.

	===A Mathematical Model===		===A Mathematical Model===
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	* The Superposition Principle is important because it makes your life easier in Physics. You can make assumptions based on the fact that the net field at any location is equal to the sum of all the individual fields. You don't know one of the individual fields, but know the net field? Simple subtraction can help you calculate each individual field. Imagine if all Electric Fields influenced each other? It'd be really difficult to calculate net electric fields without a complicated equation that takes into account one field as a function of another. yuck. Thank the Physics Gods for the Superposition Principle. Its very important to keep this idea in mind any time a net field comes up. Always remember that the independent fields are not individually effected by each other.		* The Superposition Principle is important because it makes your life easier in Physics. You can make assumptions based on the fact that the net field at any location is equal to the sum of all the individual fields. You don't know one of the individual fields, but know the net field? Simple subtraction can help you calculate each individual field. Imagine if all Electric Fields influenced each other? It'd be really difficult to calculate net electric fields without a complicated equation that takes into account one field as a function of another. yuck. Thank the Physics Gods for the Superposition Principle. Its very important to keep this idea in mind any time a net field comes up. Always remember that the independent fields are not individually effected by each other.

	~~How is it connected to your major?~~
	* Since the Superposition Principle can be applied to circuits, and since Biomedical Engineering sometimes create medical device that require circuity, knowing how to create a circuit and calculate the electric field with the superposition principle is an important tool to have. Or if you're a significantly better major like ME, this can be extremely useful in statics problems. If a system is statically determinant like this one:

	[[File:determinate-structures-18-638.jpeg]]		[[File:determinate-structures-18-638.jpeg]]
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	*[http://www.sparknotes.com/testprep/books/sat2/physics/chapter17section4.rhtml Sparknotes Explanation]		*[http://www.sparknotes.com/testprep/books/sat2/physics/chapter17section4.rhtml Sparknotes Explanation]

	*[http://www.physicsbook.gatech.edu/Superposition_Principle ~~This guy who made a Superposition principle on this wiki even though I already made one~~]		*[http://www.physicsbook.gatech.edu/Superposition_Principle]

	===External links===		===External links===

Ryany715 at 19:12, 9 April 2017

2017-04-09T19:12:19Z

← Older revision		Revision as of 15:12, 9 April 2017
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	'''Claimed by ~~Abhinav Sundaresan~~: ~~March 15~~, ~~2016~~'''		'''Claimed by Ryan Yeung: April 8, 2017'''

	This topic covers the Superposition Principle. This was the first and original article on this topic (also the best).		This topic covers the Superposition Principle. This was the first and original article on this topic (also the best). However it's now being edited, and therefore has become ever better than the best.

	==The Main Idea==		==The Main Idea==

	The superposition principle essentially states that in a given closed system, the 'reaction' of an object to outside forces is the sum of the outside force acting on it. These forces can act along multiple dimensions, therefore meaning that vector notation will be needed.		The superposition principle essentially states that in a given closed system, the 'reaction' of an object to outside forces is the sum of the outside force acting on it. These forces can act along multiple dimensions, therefore meaning that vector notation will be needed. More simply stated the principle states that the sum of a systems responses is the same as the net result of the forces taken as individuals. In order for the superposition principle to apply, the system must be linear. This means the reaction of the system follows a linear predictable pattern.

	===A Mathematical Model===		===A Mathematical Model===

	The net electric field due to two or more charges is the vector sum of each field due to each individual charge. This not only applies to Electric Fields, but Magnetic Fields as well. It is important to note that in the superposition principle, the electric field caused by a charge is not affected by the presence of other charges.		The net electric field due to two or more charges is the vector sum of each field due to each individual charge. This not only applies to Electric Fields, but Magnetic Fields as well. It is important to note that in the superposition principle, the electric field caused by a charge is not affected by the presence of other charges. It is important to note that this principle applies to all linear systems, note just those of fields. It has the same net result for mechanics as well. Below are the 2 predominate mathematical models for the principle.

	:<math>F(x_1+x_2)=F(x_1)+F(x_2) \,</math>		:<math>F(x_1+x_2)=F(x_1)+F(x_2) \,</math>
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	pluscharge = sphere(pos=vector(-5*s, 0,-s/2), radius=1e-10, color=color.red)		pluscharge = sphere(pos=vector(-5*s, 0,-s/2), radius=1e-10, color=color.red)
	minuscharge = sphere(pos=vector(-5*s, 0, s/2), radius=1e-10, color=color.blue)		minuscharge = sphere(pos=vector(-5*s, 0, s/2), radius=1e-10, color=color.blue)
	velocity = vector(4e4,0,0) # The dipoles cm velocity ~~# The dipoles cm velocity~~		velocity = vector(4e4,0,0) # The dipoles cm velocity
	robs = vector(0,s,0)		robs = vector(0,s,0)

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	Notice that this uses the principle of superposition. The magnetic and electric fields of the two particles in the dipole are added. This determines the net field at the observation location and is therefore a perfect example of superposition.		Notice that this uses the principle of superposition. The magnetic and electric fields of the two particles in the dipole are added. This determines the net field at the observation location and is therefore a perfect example of superposition. This is a very elegant and simple example of the principle. It is essentially stated here as the net force as the sum of all other forces. When using the principle in this way it is very important to note the direction of the forces, as they greatly effect the outcome of the answer.

	==Examples==		==Examples==
	<gallery widths="300px">		<gallery widths="300px">
	File:Superposition Principle.JPG\| This picture shows the electric field at the location of q3. Note that the Electric Fields of both q1 and q2 were both calculated individually (but do not react because of one another) and summed up to get the net electric field		File:Superposition Principle.JPG\| This picture shows the electric field at the location of q3. Note that the Electric Fields of both q1 and q2 were both calculated individually (but do not react because of one another) and summed up to get the net electric field. Notice the importance of the signs.
	File:1111.PNG\| Even by adding more source charges, the individual electric fields created by each source charge are unaffected by subsequent charges.		File:1111.PNG\| Even by adding more source charges, the individual electric fields created by each source charge are unaffected by subsequent charges.
	</gallery>		</gallery>
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	Therefore, the net electric field at the electron's location is <math><2\hat{i}+2\hat{j}+0\hat{k}> </math>N/C		Therefore, the net electric field at the electron's location is <math><2\hat{i}+2\hat{j}+0\hat{k}> </math>N/C. Again it is important to note the effect of the signs. Since both components have positive notation, the net result is positive. However if any of the components had a negative direction, it would have been important to note this throughout the answer.

	=== Difficult ===		=== Difficult ===
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	<math>\|\|\vec{r_2}\|\| = \sqrt{-5^2 + 0^2} =\sqrt{25}</math>		<math>\|\|\vec{r_2}\|\| = \sqrt{-5^2 + 0^2} =\sqrt{25}</math>

			Again, sign notation is very important. Note how the unit vector defines the direction of the fields in this equation and example. It is easiest to define the unit vector first. Then proceed to multiply this my the magnitude of the field, as this allows you to account for direction before the calculation of field.

	Using Coloumb's Law, you get:		Using Coloumb's Law, you get:
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	==Connectedness==		==Connectedness==
	How is this topic connected to something that you are interested in?		How is this topic connected to something that you are interested in?
	* The Superposition Principle is important because it makes your life easier in Physics. You can make assumptions based on the fact that the net field at any location is equal to the sum of all the ~~invidiual~~ fields. You don't know one of the individual fields, but know the net field? Simple subtraction can help you calculate each individual field. Imagine if all Electric Fields influenced each other? It'd be really difficult to calculate net electric fields without a complicated equation that takes into account one field as a function of another. yuck. Thank the Physics Gods for the Superposition Principle.		* The Superposition Principle is important because it makes your life easier in Physics. You can make assumptions based on the fact that the net field at any location is equal to the sum of all the individual fields. You don't know one of the individual fields, but know the net field? Simple subtraction can help you calculate each individual field. Imagine if all Electric Fields influenced each other? It'd be really difficult to calculate net electric fields without a complicated equation that takes into account one field as a function of another. yuck. Thank the Physics Gods for the Superposition Principle. Its very important to keep this idea in mind any time a net field comes up. Always remember that the independent fields are not individually effected by each other.

	How is it connected to your major?		How is it connected to your major?
	* Since the Superposition Principle can be applied to circuits, and since Biomedical Engineering sometimes create medical device that require circuity, knowing how to create a circuit and calculate the electric field with the superposition principle is an important tool to have.		* Since the Superposition Principle can be applied to circuits, and since Biomedical Engineering sometimes create medical device that require circuity, knowing how to create a circuit and calculate the electric field with the superposition principle is an important tool to have. Or if you're a significantly better major like ME, this can be extremely useful in statics problems. If a system is statically determinant like this one:

			[[File:determinate-structures-18-638.jpeg]]

			In a system such as this, the superposition principle is especially useful for finding the individual reactions at each point on the beam as it is known that the net reaction for the entire system is 0.

	Is there an interesting industrial application?		Is there an interesting industrial application?
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	[https://www.youtube.com/watch?v=S1TXN1M9t18 Instructional video on how to calculate the net electric field using the superposition principle]		[https://www.youtube.com/watch?v=S1TXN1M9t18 Instructional video on how to calculate the net electric field using the superposition principle]

			[https://www.youtube.com/watch?v=_8fcT95JV34 Video detailing the general use of the principle]

	==References==		==References==

	Chabay, Ruth W.; Sherwood, Bruce A. (2014-12-23). Matter and Interactions, 4th Edition: 1-2 (Page 522). Wiley. Kindle Edition.		Chabay, Ruth W.; Sherwood, Bruce A. (2014-12-23). Matter and Interactions, 4th Edition: 1-2 (Page 522). Wiley. Kindle Edition.

			https://www.slideshare.net/tarungehlot1/determinate-structures

	[[Fields]]		[[Fields]]

Ksomu3 at 20:14, 24 November 2016

2016-11-24T20:14:51Z

← Older revision		Revision as of 16:14, 24 November 2016
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	'''Claimed by Abhinav Sundaresan: March 15, 2016'''		'''Claimed by Abhinav Sundaresan: March 15, 2016'''

	~~'''Claimed by Kavin Somu Fall 2016'''~~

	This topic covers the Superposition Principle. This was the first and original article on this topic (also the best).		This topic covers the Superposition Principle. This was the first and original article on this topic (also the best).

Ksomu3 at 05:49, 24 November 2016

2016-11-24T05:49:26Z

← Older revision		Revision as of 01:49, 24 November 2016
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	'''Claimed by Abhinav Sundaresan: March 15, 2016'''		'''Claimed by Abhinav Sundaresan: March 15, 2016'''

			'''Claimed by Kavin Somu Fall 2016'''

	This topic covers the Superposition Principle. This was the first and original article on this topic (also the best).		This topic covers the Superposition Principle. This was the first and original article on this topic (also the best).

Asundaresan6: /* Simple */

2016-04-17T06:42:16Z

Simple

← Older revision		Revision as of 02:42, 17 April 2016
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	===Simple===		===Simple===

			[[File:Electric_Forces_Fields_P1.JPG]]

	Say that we have two positive particles at the above locations. Ignore the charges and distance provided for now. The electric field at the location of the negative charge is <math>\vec{E_1} = <2\hat{i}+0\hat{j}+0\hat{k}> </math>N/C and <math>\vec{E_2} = <0\hat{i}+2\hat{j}+0\hat{k}> </math>N/C. What is the net electric field at the location of the electron? Use the principle of superposition.		Say that we have two positive particles at the above locations. Ignore the charges and distance provided for now. The electric field at the location of the negative charge is <math>\vec{E_1} = <2\hat{i}+0\hat{j}+0\hat{k}> </math>N/C and <math>\vec{E_2} = <0\hat{i}+2\hat{j}+0\hat{k}> </math>N/C. What is the net electric field at the location of the electron? Use the principle of superposition.

Asundaresan6: /* Simple */

2016-04-17T06:39:01Z

Simple

← Older revision		Revision as of 02:39, 17 April 2016
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	Therefore, the net electric field at the electron's location is <math><2\hat{i}+2\hat{j}+0\hat{k}> </math>		Therefore, the net electric field at the electron's location is <math><2\hat{i}+2\hat{j}+0\hat{k}> </math>N/C

	=== Difficult ===		=== Difficult ===

Asundaresan6: /* Simple */

2016-04-17T06:38:21Z

Simple

← Older revision		Revision as of 02:38, 17 April 2016
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	===Simple===		===Simple===

	Say that we have two positive particles at the above locations. Ignore the charges and distance provided for now. The electric field at the location of the negative charge is <math>\vec{E_1} = <2\hat{i}+0\hat{j}+0\hat{k}> </math>N/C and <math>\vec{E_2} = <0\hat{i}+2\hat{j}+0\hat{k}> <math>N/C		Say that we have two positive particles at the above locations. Ignore the charges and distance provided for now. The electric field at the location of the negative charge is <math>\vec{E_1} = <2\hat{i}+0\hat{j}+0\hat{k}> </math>N/C and <math>\vec{E_2} = <0\hat{i}+2\hat{j}+0\hat{k}> </math>N/C. What is the net electric field at the location of the electron? Use the principle of superposition.
	What is the net electric field at the location of the electron? Use the principle of superposition.

	'''Answer:'''		''Answer:''

	Since we know the electric fields from both particles at the point, the superposition principle tells us that we must add the fields together to find the net field. Doing this gives us:		Since we know the electric fields from both particles at the point, the superposition principle tells us that we must add the fields together to find the net field. Doing this gives us:
	<math>\vec{E_1} + vec{E_2} = <2\hat{i}+0\hat{j}+0\hat{k}> <math>N/C + <math>\<0\hat{i}+2\hat{j}+0\hat{k}> <math>N/C		<math>\vec{E_1} + \vec{E_2} = <2\hat{i}+0\hat{j}+0\hat{k}> </math>N/C + <math><0\hat{i}+2\hat{j}+0\hat{k}> </math>N/C
	<math> = <2\hat{i}+2\hat{j}+0\hat{k}> <math>		<math> = <2\hat{i}+2\hat{j}+0\hat{k}> </math>


	Therefore, the net electric field at the electron's location is <math><2\hat{i}+2\hat{j}+0\hat{k}> <math>		Therefore, the net electric field at the electron's location is <math><2\hat{i}+2\hat{j}+0\hat{k}> </math>

	=== Difficult ===		=== Difficult ===

Asundaresan6: /* Examples */

2016-04-17T06:28:55Z

Examples

← Older revision		Revision as of 02:28, 17 April 2016
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	===Simple===		===Simple===

			Say that we have two positive particles at the above locations. Ignore the charges and distance provided for now. The electric field at the location of the negative charge is <math>\vec{E_1} = <2\hat{i}+0\hat{j}+0\hat{k}> </math>N/C and <math>\vec{E_2} = <0\hat{i}+2\hat{j}+0\hat{k}> <math>N/C
			What is the net electric field at the location of the electron? Use the principle of superposition.

			'''Answer:'''

			Since we know the electric fields from both particles at the point, the superposition principle tells us that we must add the fields together to find the net field. Doing this gives us:
			<math>\vec{E_1} + vec{E_2} = <2\hat{i}+0\hat{j}+0\hat{k}> <math>N/C + <math>\<0\hat{i}+2\hat{j}+0\hat{k}> <math>N/C
			<math> = <2\hat{i}+2\hat{j}+0\hat{k}> <math>


			Therefore, the net electric field at the electron's location is <math><2\hat{i}+2\hat{j}+0\hat{k}> <math>
	=== Difficult ===		=== Difficult ===

Asundaresan6: /* Examples */

2016-04-17T06:21:02Z

Examples

← Older revision		Revision as of 02:21, 17 April 2016
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	File:1111.PNG\| Even by adding more source charges, the individual electric fields created by each source charge are unaffected by subsequent charges.		File:1111.PNG\| Even by adding more source charges, the individual electric fields created by each source charge are unaffected by subsequent charges.
	</gallery>		</gallery>

			===Simple===