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 …………..

Options

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

Answer

A

Explanation

Length of diagonal of a cube of side `b=sqrt(3)b`
Distance of centre of cube from each vertex `=(sqrt(3)b)/(2)`
P.E of given system of charge `U=8xx(1)/(4piepsilon_(0))((-q)(q))/((sqrt(3)b)/2)=(-4q^(2))/(sqrt(3)piepsilon_(0)b)`