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Electricity and Magnetism

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Change in Potential Energy from Adding Like Charge to a System

EANDM-TEYPSR

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 three point charges, each with a potential $+q$ placed upon them, all separated from one another by a distance $r$.

The potential energy of this configuration is $U_{+++}$.

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

Both potentials energies are zero when all charges are infinitely far apart.

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

A

$R = 2$

B

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

C

$R = \cfrac{1}{2}$

D

$R = 3$