Consider a block of conducting material of resistivity p shown in the figure. Current I enters at A and leaves from D. We apply superposition principle to find voltage `Delta 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 filed E(r) at distance r from A by using Ohm’s law `E=pi` 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 result for A and D.
`Delta v`measured between B and C is :

Options

A. `(pI)/(2pi r^2)`
B. `(pI)/(8pir^2)`
C. `(p I)/pi^2`
D. `(pI)/(4 pi r^2)`

Explanation

We define electric field as `E=pj implies E=(jD)(2pir^2)`