Charge distribution

Gauss's Law

 

If you are actually going to use Gauss's law to prove this you'd better state the problem a lot more precisely. Is the sphere conducting? Does the sphere have any net charge on it? Otherwise, it's not even true.

 

Yes, I guess I made some assumptions about the problem. So can you tell us more?

 

Any ideas? We are only supposed to help you, not work the problem for you. If nothing else comes to mind, state Gauss' law.

 

Take a gaussian surface inside the conductor. Tells you total charge enclosed is zero - so there's a surface charge on the cavity surface cancelling the enclosed charge. Now take a gaussian outside the conductor. The field must correspond to the charge in the cavity since the conductor is net neutral. So there's a surface charge on the outside equal to the charge in the cavity. You can argue that the charge distribution on the outside of the sphere is uniform since there is no field coming through the conductor to the outer surface to disturb it.