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

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
$U=8 \times\left\{\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{(-q)(q)}{\sqrt{3} b / 2}\right\}$
$=\frac{-4 q^{2}}{\sqrt{3} \pi \varepsilon_{0} b}$