A potential difference V is applied across a conductor of length l and cross- sectional area A. Briefly explain how the current density j in the…

Current density $\displaystyle j = \dfrac{ne^2 E\tau}{m}$

$\displaystyle = \dfrac{ne^2 V\tau}{ml}$

Or $\displaystyle j \propto V$

If $\displaystyle V$ is doubled, the current density will be doubled.

As the conductor were gradually stretched to reduce its cross sectional area to half $\displaystyle (A/2)$, its length will become double $\displaystyle (2l)$ as volume of conductor remains the same.

$\displaystyle \because\ j \propto \dfrac{1}{l}$

$\displaystyle \therefore$ If same potential difference is applied, the current density will become half.