A conductor, with outer surface labelled a, contains a cavity, inner surface b. In this cavity there is a conducting sphere of radius r, and surface c. The sphere carries a charge of 1 C, while the conductor a charge of 2 C. Determine the charges on surfaces a, b, and c respectively. Express the answer in coulombs.

Explanation:

At the center of the conductor  lies the sphere of radius r which contains charge 1C . The sphere is a conductor so all its charge will lie on its surface . Hence on surface c charge lying = 1 C .

Charge on surface c will induce a charge - 1C on inner surface of hollow outer conductor so charge on inner surface b of the hollow conductor will b - 1 C .

Here it is to be noted that the charge carried by hollow conductor will lie on its surface . so on surface a of hollow conductor , its charge 2C will lie . Apart from it a charge + 1 C will also be induced on it due to charge on the inner sphere . Hence total charge on surface a will be 2C +1C = +3C .