Q. If identical charges $( - q)$ are placed at each corner of a cube of side $b,$ then electric potential energy of charge $( + q)$ which is placed at centre of the cub will be
A) $\frac{8\sqrt{2}q^{2}}{4\pi\varepsilon_{0}b}$
B) $\frac{- 8\sqrt{2}q^{2}}{\pi\varepsilon_{0}b}$
C) $\frac{- 4\sqrt{2}q^{2}}{\pi\varepsilon_{0}b}$
D) $\frac{- 4q^{2}}{\sqrt{3}\pi\varepsilon_{0}b}$
Explanation
(d) Length of the diagonal of a cube having each side $b$ is $\sqrt{3}b.$ So distance of centre of cube from each vertex is $\frac{\sqrt{3}b}{2}$
Hence potential energy of the given system of charge is
$U = 8 \times \left\lbrack \frac{1}{4\pi\varepsilon_{0}}.\frac{( - q)(q)}{\sqrt{3}b/2} \right\rbrack = \frac{- 4q^{2}}{\sqrt{3}\pi\varepsilon_{0}b}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.