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 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 $E\left(r\right)$ at distance $r$ from $A$ by using ohm's law $E=\rho j$, where $r$ is the current per unit area at $r$.
iii) From the $r$ dependence of $E\left(r\right)$, obtain the potential $E\left(r\right)$ 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