Question

A hollow metal sphere is electrically neutral (no excess charge). A small amount of negative charge is suddenly placed at one point P on this metal sphere. If we check on this excess negative charge a few seconds later we will find one of the following possibilities: a. All of the excess charge remains right around P. b. The excess charge has distributed itself evenly over the outside surface of the sphere. c. The excess charge is evenly distributed over the inside and outside surface. d. Most of the charge is still at point P, but some will have spread over the sphere. e. There will be no excess charge left.

Answer 1

Answer and explanation:

The right answer is b) "The excess charge has distributed itself evenly over the outside surface of the sphere".

The hollow metal sphere is a conductor. This means that charges can move freely over its surface. On the other side, a metal body act as an equipotential body. Once some charge is set and there is no voltage differential imprinted over the body, to keep being an equipotential body the charges must distribute evenly on the external surface. Must not exist charge in the volume, or would exist an electrical field and therefore a voltage differential. Also, the charge distribution in the internal surface must be null. If you apply gauss theorem with a gaussian sphere with a radius between the internal and external surface, knowing that field E is null, the enclosed charge must be null.