The electric field $E$, current density $J$ and conductivity $\sigma$ of a conductor are related as
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(b) Let $I$ current flow through a conductor when applied potential difference $V$ volt. then, from ohm's law,
$I=\frac{V}{R}$
But $R=\rho \frac{L}{A}$
Therefore,
$I=\frac{V}{\rho \frac{L}{A}}$
$\Longrightarrow \frac{I}{A}=\frac{V}{\rho L}$
but, $\frac{I}{A}=J, \frac{V}{L}=E$
Hence, $J=\sigma E$
$\Longrightarrow \sigma=\frac{J}{E}$
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