Question

Four point charges are located on the corners of the square with the side of 40cm. Three charges are 1 μC and one is -1 μ C. Find the electric potential at the center of the square (Assume that the potential at infinity is zero)

Answer 1

Length of each side of the square is 40 cm or 0.4 m.

Hence, the center of the square is d = ( 0.4 / 2 ) m, or, 0.283 m away from any corner.

A charge of q = 1 C = 10^-6 C is placed at three of the corners of the square, and, a charge - q = - 10⁶ C is placed at the fourth one.

Hence, electric potential at the center of the square is :

V = ( 1 / 4_o ) ( 3 x q / d - q / d ) = ( 1 / 4_o ) ( 2q / d ),

where, _o is the permittivity of free space = 8.854 x 10^-12 S.I.,

1 / 4_o = 9 x 10⁹ S.I.

Plugging all the known values : V = ( 9 x 10⁹ x 2 x 10^-6 / 0.283 ) V = 6.36 x 10⁴ V.

Hence, the electric potential at the center of the square is 6.36 x 10⁴ V.