A spherical conducting shell of inner radius r₁ and outer radius r₂ has a charge Q.
i) 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?
ii) Is the electric field inside a cavity (with no charge) zero, even if the shell is not spherical, but has any irregular shape? Explain.

As a ‘+ q’ charge place at the centre of the shell, it will create a ‘–q’ charge on the inner surface of the shell.
The charge on the outer surface will increase by + q due to the –q charge on the inner surface by induction. Therefore, there will be total (Q + q) charge on the outer surface of the shell and –q charge on the inner surface of the shell.

Now surface area of inner surface 
and surface area of outer surface 
Thus, charge density on the outer surface  
and charge density on the inner surface