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Electricity and Magnetism

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Potential of Two Identical Charges on a Line at the Origin

EANDM-$EG@98

Figure 1 depicts a pair of negatively charged particles, each having a charge of $-q$, arrayed along the $\hat{x}$ axis, symmetrically about the origin.

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

What is the electric potential $V$ at the origin of the $\hat{x}$ axis? Take $k = 8.99 \times 10^9 \text{ N} \cdot \text{ m}^2 / \text{C}^2$ as the electric force constant.

A

$V = -\frac{2kq}{a}$

B

$V = -\frac{4kq}{a}$

C

$V = 0$

D

$V = -\frac{8kq}{a^2}$