A charge Q is placed at the centre of an uncharged, hollow metallic sphere of radius a. (a) Find the surface charge density on the inner surface and on the outer surface. (b) If a charge q is put on the sphere, what would be the surface charge densities on the inner and the outer surface?

Explanation

Given : A sphere is uncharged metallic
sphere . Due to inductin the charge
induced at the inner surface = - q and that
in outer surface =+q
(a) Hence the surface charge density at
inner and outer surface.
= charge/ total surface area
`= - q / 4 pi (a^2) and q / 4 pi (a^2) respectively `
` (b) Again if another charge Q is added to
the surface,
We have inner surface charge density
` = - q/ 4 pi (a^2).
Because the added charge does not affect
it on the other hand the external surface
charge density = `(q+Q /4m^2)` as the Q gets
added up
(c) For electric field let us assume in
imaginary surface area inside the surface
at a distance x from centre this is same in
both the cases as the q is ineffective.
` Now, E.ds = q/epsilon_0`
` So, E= q/epsilon_0 xx 1/4pi x^2 = (Q/ 4pi epsilon_0(x^2))`.