Question

A spherical conducting shell of inner radius r₁ and outer radius r₂ has a charge Q. A charge q is placed at the centre of the shell. 

(a) What is the surface charge density on the (i) inner surface, (ii) outer surface of the shell? 

(b) Write the expression for the electric field at a point x > r₂ from the centre of the shell. 

Answer 1

(a) (i) Surface charge density on the inner surface of shell is 

σ_in = -q/4πr₁²

(ii) Surface charge density on the outer surface of shell is 

σ_out = Q+ q/4πr₂²

(b) Using, Gauss’s law E(x) = 1/4πε₀ .Q+q/x²