A long round wire of radius 'a' and conductivity is coated with material of conductivity .the thickness of the coating is 'a' . If the resistance per unit length of the coated wire is 50 % of that of the uncoated wire, determine in terms of a .Also determine the ratio of the current densities in the core and the coating and verifies that the electric field is same in the two parts.

Solution : Let R₁be the resistance per unit length of the uncoated wire.