There are eight corners of a cube and in each corner there is a charge of (−q). At the centre of the corner there is a charge of (+q) Each corner is equidistant from the centres of the cube and the distance (d) is half of the diagonals of the cube. Diagonal of the cube =√b2+b2+b2=√3b ∴d=
√3b
2
Now, electric potential energy of the charge (+q) due to a charge (−q) at one corner =U =
q1q2
4πε0r
=
(+q)×(−q)
4πε0(√3b∕2)
=−
q2
2πε0(√3b)
∴ Total electric potential energy due to all the eight identical charges =8U=