Question

Show that, if there are any unbalanced, static charges on an isolated conductor, they must reside on its surface.

Answer 1

All unbalanced, static charges on an isolated conductor reside on its surface because of the reason as per gauss's law the magnitude of electric field on the gassusian surface must be zero. As a result of which all the charges moves completely towards the surface.

Answer 2

Choose a gaussian surface that everywhere lies just inside the conductor surface.

We know that the electric field must be zero, everywhere on this gaussian surface so that the flux of E over this surface is zero.

Mathematically if electric field be E and surface area is s then flux is E.s , as E is zero ,so E.s must be zero.

So, by Gauss’s law, there can be no internal net charge. It follows that if a net charge does reside on the body, it can be distributed only over the surface layer of that body.

So, if there are any unbalanced, static charges on an isolated conductor, they must reside on its surface.