Ohm's Law, Resistivity & Temperature question from JEE Main 2008 (AIEEE)

Consider a block of conducting material of resistivity $\text{'}\rho\text{'}$ shown in the figure. Current $\text{'}I\text{'}$ enters at $\text{'}A\text{'}$ and leaves from $\text{'}D\text{'}$. We apply superposition principle to find voltage $\text{'}\Delta V\text{'}$ developed between $\text{'}B\text{'}$ and $\text{'}C\text{'}$. The calculation is done in the following steps:

(i) Take current $\text{'}I\text{'}$ entering from $\text{'}A\text{'}$ and assume it to spread over a hemispherical surface in the block.

(ii) Calculate field $E(r)$ at distance $\text{'}r\text{'}$ from A by using Ohm's law $E = \rho j,$ where $j$ is the current per unit area at $\text{'}r\text{'}$.

(iii) From the $\text{'}r\text{'}$ dependence of $E(r)$, obtain the potential $V(r)$ at $r$.

(iv) Repeat (i), (ii) and (iii) for current $\text{'}I\text{'}$ leaving $\text{'}D\text{'}$ and superpose results for $\text{'}A\text{'}$ and $\text{'}D\text{'}.$

For current entering at $A,$ the electric field at a distance $\text{'}r\text{'}$ from $A$ is