Paragraph: Consider a block of conducting material of resistivity ' $\rho$ ' 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 field $E(r)$ at distance ' $r$ ' from $A$ by using Ohm's law $E = \rho j$, 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'.
Question: $\Delta V$ measured between B and C is
(1) $\frac { \rho I } { \pi a } - \frac { \rho I } { \pi ( a + b ) }$
(2) $\frac { \rho I } { a } - \frac { \rho I } { ( a + b ) }$
(3) $\frac { \rho I } { 2 \pi a } - \frac { \rho I } { 2 \pi ( a + b ) }$
(4) $\frac { \rho I } { 2 \pi ( a - b ) }$