A charge Q is placed at the centre of an uncharged, hollow metallic sphere of radius of rasius alpha. (a) Find the surface charge density on the inner surface and on the outer surface. (b) If a charge q is pur on the sphege, what would be the surface charge dendities on the inner and the outer surface? (c) Find the electric field inside the sphere at a distance x from the centre in the situations (a) and (b).

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))`.