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)
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 / 4o ) ( 3 x q / d - q / d ) = ( 1 / 4o ) ( 2q / d ),
where, o is the permittivity of free space = 8.854 x 10-12 S.I.,
1 / 4o = 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.
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