A spherical conducting shell of inner radius r 1 and outer radius r 2 has a charge Q. (a) A charge q is placed at the centre of the shell. What is the surface charge density on the inner and outer surfaces of the shell? (b) Is the electric field inside a cavity (with no charge) zero, even if the shell is not spherical, but has any irregular shape? Explain.

Question

Philoid · Accepted Answer

(a) Charge placed at the centre of the sphere is + q. Thus, charge induced on the inner surface be –q.

Surface charge density at the inner surface of the sphere,

σ₁ = =

Charge placed at the centre of the sphere is + q. Thus, charge induced on the inner surface be + q and surface charge distribution is Q. Therefore Total charge = Q + q.

Surface charge density at the outer surface of the sphere,

σ₂ = =

(b) Yes

Whatever the shape of the shell, the electric field intensity in the cavity is zero. Take a closed loop such that it is inside the cavity and in conductor. Net work done in carrying charge along closed loop by electric field is zero. Thus, electric field is zero, whatever the shape.