A doubt in potential of a conductor

Question

Some charge is being given to a conductor. Then, its potential :
a) is max.m at the surface.
b) is max.m at the centre.
c) remains same throughout the conductor.
d) is max.m somewhere b/w the surface and centre.

Ans)C

1) pl. Explain how...

2) what if it was a nonconductor?what would be the answer then? how?

3) would there be any effect of the shape of the conductor on the answer?

Thank you.

Answer 1

(1)  An electric conductor is an equipotential volume, which means that its electric potential is the same everywhere inside its volume (C) and along its surface, unless an external electric field is applied to it.  If there are free charges in a conductor, they repel each other and migrate toward the surface, and spread out in such a way that the potential is constant over the surface and throughout the interior.  Free charges simply distribute themselves to cancel out any electric field in the interior of the conductor, which keeps the electric potential the same throughout.  A detailed explanation requires getting into Gauss' law.  Have you seen this law in your physics class?  However, the electric potential in the region of space exterior to the conductor changes as charge is supplied to the conductor.  But the question asked about changes in potential inside the conductor and on its surface.

 

(2)  In the case of a nonconductor, the charges do not redistribute to cancel interior electric fields, so the presence of charges can set up a net electric field inside the nonconductor.  The presence of an electric field indicates a region where the electric potential is varying over distance.

 

(3)  If the boundary surface of the conductor is "simply connected" (i.e. has no holes in it), the shape of the conductor does not matter.  But if it has holes, then it matters.  Usually we consider only simply connected boundary surfaces.  This goes back to use of Gauss' law to perform the calculations.