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Electricity and Magnetism

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Location Dependence of Potential Energy of Five Charged Particles

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Figure 1 depicts five charges, arranged on a square of side length $a$.

Figure 1. Timothy Black. Created for Albert.io. Copyright 2016. All rights reserved.

Four of the charges have a positive charge $+q$, a​nd one has a charge $-q$. The four positive charges are located at the corners of the square, and the negative charge is in the center of the square. We can call this configuration of charges configuration $A$.

Figure 2 also depicts five charges, arranged on a square of side length $a$, so that four of the charges have a positive charge $+q$ and one has a charge $-q$.

Figure 2. Timothy Black. Created for Albert.io. Copyright 2016. All rights reserved.

In this case, the central negative charge has swapped places with the positive charge in the lower left-hand corner. Let us call this configuration of charges configuration $B$.

The potential energy of configuration $A$ is

the potential energy of configuration $B$.