Question

Four equal charges q1 are situated at the corners of a square. The sides of the square are length a.

1) What is the net force on a charge q2 placed at the center of the square?

2) What is the electric potential at the center of the square?

3) Suppose one of four q1's is removed. Now whatis the net force on q2?

Answer 1

Electric force is given by

F = kQ1Q2/d^2

Electric Potential is given by

P = kQ/d^2

here d = distance between center and one corner of square = diagonal/2 = sqrt(2)*a/2 = a/sqrt(2)

1)

magnitude of force due to q1 at q2 = kq1q2/(a/sqrt(2))^2 = 2*kq1q2/a^2

magnitude of force is same for all for charges q1 and direction of forces due to diagonal charges is opposite.means net force at center is zero.

2)

electric potential at center due to q1 charge = kq1/(a/sqrt(2))^2 = 2*kq1/a^2

electric potential due to all q1 is same at center.

net electric potential at center = 4*(2*kq1/a^2) = 8*kq1/a^2

3)

one q1 is removed so now net force on q2 at center of square

F = 2*kq1q2/a^2

because electric force due to two diagonal charge will be cancled.