Consider a block of conducting material of resistivity $\rho$ shown in the figure. Current $I$ enters at $A$ and leaves from $D$. We apply the superposition principle to find the 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 the 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 $D$. $\Delta V$ measured between $B$ and $C$ is

• A
  $\frac{\rho I}{2 \pi(a-b)}$
• B
  $\frac{\rho I}{\pi a}-\frac{\rho I}{\pi(a+b)}$
• C
  $\frac{\rho I}{a}-\frac{\rho I}{(a+b)}$
• D
  $\frac{\rho I}{2 \pi a}-\frac{\rho I}{2 \pi(a+b)}$