Given., length of side of cube = b
and charge at each side of its vertices = q
As we know,
the length of diagonal of the cube side, d = √(b2 + b2) = √(2b2)= b√2
Let l be the length of diagonal of cube. Thus,
l = √(d2 + b2)
Distance between center of cube and vertices, r = l/2
r = (b√3)/2
The electric potential (V) at the centre of the cube is due to the presence of 8 charges at the vertices.
The electric field intensity at the center due to all the eight charges is zero because the fields due to the presence of charges at the vertices cancel in pairs.