AIEEE 2008 Solved Paper

Consider a block of conducting material of resistivity ‌′ρ′ shown in the figure. Current ‌′I′ enters at ‌′A′ and leaves from ‌′D′. We apply superposition principle to find voltage ' ∆V′ developed between ‌′B′ and ‌′C′. The calculation is done in the following steps:
(i) Take current ‌′I′ entering from ‌′A′ and assume it to spread over a hemispherical surface in the block.
(ii) Calculate field E(r) at distance ‌′r′ from A by using Ohm's law E=ρj, where j is the current per unit area at ‌′r′.
(iii) From the ‌′r′ dependence of E(r), obtain the potential V(r) at r.
(iv) Repeat (i), (ii) and (iii) for current ' I′ leaving ‌′D′ and superpose results for ‌′A′ and ‌′D′.For current entering at A, the electric field at a distance ' r' from A is