a cube of side b have charge q at each vertices. determine the potential and electric field due to this charge array at the center of cube.

 There are 8 vertices in the cube then the 8 charges are available there.

           We all know that the diagonal of the square is √3b

          Distance between the center and the corner of the cube is √3b/2.

     Potential due to single charge = kq/r  = 2kq/√3b

Potential due to 8 charge = 16kq/√3b

Electric Field at the center due to the 8 charges get cancelled. This is because the charges are distributed symmetrically with respect to the centre of the  square. Hence electric field will be zero.