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Electricity and Magnetism

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Moderate

Coulomb Force with Three Charges

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Two positive charges, each with charge $+Q$, are separated by a distance $2L$. A charge $-Q$ is located at a distance $d$ perpendicular to the midpoint of a line between the two positive charges. The arrangement is shown in the figure below.

Created for Albert.io. Copyright 2016. All rights reserved.

Which expression below represents the magnitude of the net force $F_N$ that acts on the negative charge?

A

$F_N = \cfrac{1}{2 \pi \epsilon_o} \cfrac {d \:Q^2}{ {(L^2 +d^2)^{ 1/2}}}$

B

$F_N = \cfrac{1}{2 \pi \epsilon_o} \cfrac {d \: Q^2}{ {(L^2 +d^2)}}$

C

$F_N = \cfrac{1}{2 \pi \epsilon_o} \cfrac {d \: Q^2}{ {(L^2 +d^2)^{ 3/2}}}$

D

$F_N = \cfrac{1}{2 \pi \epsilon_o} \cfrac {d \: Q^2}{ {(d^2)^{ 3/2}}}$

E

$F_N = \cfrac{1}{4 \pi \epsilon_o} \cfrac {d \: Q^2}{ {(L^2 +d^2)^{ 3/2}}}$