Electrostatic Potential and Capacitance - Result Question 20
22. Each corner of a cube of side $l$ has a negative charge, $-q$. The electrostatic potential energy of a charge $q$ at the centre of the cube is [2002]
(a) $-\frac{4 q^{2}}{\sqrt{2} \pi \varepsilon_0 l}$
(b) $\frac{\sqrt{3} q^{2}}{4 \pi \varepsilon_0 l}$
(c) $\frac{4 q^{2}}{\sqrt{2} \pi \varepsilon_0 l}$
(d) $-\frac{4 q^{2}}{\sqrt{3} \pi \varepsilon_0 l}$
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Answer:
Correct Answer: 22. (d)
Solution:
- (d) Length of body diagonal $=\sqrt{3} \ell$
$\therefore$ Distance of centre of cube from each corner
$r=\frac{\sqrt{3}}{2} \ell$
P.E. at centre
$=8 \times$ Potential Energy of the charge $(+q)$ due to charge $(-q)$ at one corner
$=8 \times \frac{K q \times(-q)}{r}$
$=8 \times \frac{1}{4 \pi \varepsilon_0 \sqrt{3} l} \times 2 \times q \times(-q)=\frac{-4 q^{2}}{\sqrt{3} \pi \varepsilon_0 l}$
