Question

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 cube will be

• A. $\frac{8\sqrt{2}{q}^2}{4\pi {\epsilon }_{0}b}$
• B. $\frac{-8\sqrt{2}{q}^2}{\pi {\epsilon }_{0}b}$
• C. $\frac{-4\sqrt{2}{q}^2}{\pi {\epsilon }_{0}b}$
• D. $\frac{-4q^2}{\sqrt{3}\pi {\epsilon }_{0}b}$

Answer 1

Answer: (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 potentialenergy of the given system of charges is
$U=8\times \left\{\frac{1}{4\pi {\epsilon }_0}\cdot \frac{(-q)(q)}{\sqrt{3}b/2}\right\}$
$=\frac{-4q^2}{\sqrt{3}\pi {\epsilon }_{0}b}$