If identical charges `(-q)` are placed at each corner of a cube of side `b`, then electric potential energy of charge `(+q)` which is palced at centre of the cube will be

Options

A. `(8sqrt(2)q^(2))/(4pi epsilon_(0)b)`
B. `(-8sqrt(2)q^(2))/(pi epsilon_(0)b)`
C. `(-4sqrt(2)q^(2))/(pi epsilon_(0)b)`
D. `(-4q^(2))/(sqrt(3)pi epsilon_(0)b)`

Answer

D

Explanation

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 `(sqrt(3) b)/(2)`.
Hence potential, energy of the given system of change is
`U = 8 xx {(1)/(4pi epsilon_(0)).((-q)(q))/(sqrt(3)b//2)} = (-4q^(2))/(sqrt(3)pi epsilon_(0))`