Question

A conducting sphere of radius R carries a charge Q. Another conducting sphere has a radius R/2, but carries the same charge.

Answer 1

It is known that the charge would flow between the circuits till potential becomes equal on both of the spheres.

Assume, a charge x flows. Hence the charge on the larger sphere would be x and the charge on the smaller sphere would be Q – x.

Potential on the smaller sphere = k (Q - x) / R and Potential on the larger sphere = k x /2R.

Equating the potentials we can write, k (Q - x) / R = k x /2R or, Q - x = x/2 or, 3x/2 = Q or, x = 2Q/3. Therefore a charge of 2Q/3 would flow between them.