Question

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

Answer 1

The electric field inside the sphere at a distance x from the centre is E = [Q / 4 π ε0 ( x^2)]

Explanation:

• A sphere is uncharged metallic  sphere.
• Due to induction 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.

Surface charge density  = charge/ total surface area

Surface charge density = - q / 4π (a^2) and q / 4π (a^2) respectively.

(b) We have 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 / 4 m^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 / ε0

So, E = q / ε0 × 1 / 4πx^2 = [Q / 4 π ε0 ( x^2)]

Hence the electric field inside the sphere at a distance x from the centre is E = [Q / 4 π ε0 ( x^2)]