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Electricity and Magnetism

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Change in Potential Energy from Adding Unlike Charge to a System

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Figure 1 depicts two point charges, each with a charge of $+q$ placed upon it, separated from one another by a distance $r$. The potential energy of this configuration is $U_{++}$.

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

Figure 2 depicts the same two charges from Figure 1, in addition to a third charge $-q$.

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

All three charges are separated from one another by a distance $r$. The potential energy of this configuration is $U_{++-}$. Both potential energies are zero when all charges are infinitely far apart.

What is the ratio $R = \cfrac{U_{++-}}{U_{++}}$?

A

$R = 1$

B

$R = -1$

C

$R = \cfrac{3}{2}$

D

$R = -\cfrac{3}{2}$