Question

Obtain the equation $\overrightarrow{J}=\sigma \overrightarrow{E}$ of Ohm's law on the basis of drift velocity. (Where symbols carry their usual meanings).

Answer 1

From Ohm's law,

$I=\frac{V}{R}$

$⟹J=\frac{I}{A}=\frac{V}{RA}$

$=\frac{El}{\frac{\rho l}{A}A}$

$=\frac{El}{\rho l}$

$=\frac{E}{\rho }=\sigma E$

Hence in vector form,

$\overrightarrow{J}=\sigma \overrightarrow{E}$