Electrostatics Question 795
Question: Each corner of a cube of side l has a negative charge, -q. The electrostatic potential energy of a charge q at the center of the cube is
Options:
A) $ -\frac{4q^{2}}{\sqrt{2}\pi {\varepsilon _{0}}l} $
B) $ \frac{\sqrt{3}q^{2}}{4\pi {\varepsilon _{0}}l} $
C) $ \frac{4q^{2}}{\sqrt{2}\pi {\varepsilon _{0}}l} $
D) $ -\frac{4q^{2}}{\sqrt{3}\pi {\varepsilon _{0}}l} $
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Answer:
Correct Answer: D
Solution:
[d] Length of body diagonal $ =\sqrt{3}\ell $
$ \therefore $ Distance of center of cube from each comer $ r=\frac{\sqrt{3}}{2}\ell $
$ \text{P}\text{.E}\text{. at center= 8 }!!\times!!\text{ Potential Energy due to} $
$ A=8\times \frac{Kq\times ( -q )}{r} $
$ =8\times \frac{1}{4\pi {\varepsilon _{0}}\sqrt{3}\ell }\times 2\times q\times ( -q )=\frac{-4q^{2}}{\sqrt{3}\pi {\varepsilon _{0}}\ell } $
