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

Answer

`(-4 q^2)/(pi epsilon_0 sqrt(3) b)`

Explanation

Length of the cube diagonal is `sqrt(3) b`. Distance of center of the cube from its each corner is
`r = (sqrt(3))/(2) b`
Total PE of charge q at the center is
`(-8 q(q))/(4 pi epsilon_0 r) = (-8 q^2)/(4 pi epsilon_0 sqrt(3)(b //2))= (-4q^2)/(pi epsilon_0 sqrt(3) b)`.