Question

For a metallic conductor, what is the relation between current density $\left(j\right)$, conductivity $\left(\sigma \right)$ and electric field Intensity $E$?

Answer 1

For metallic conductor, if specific resistance is $\rho$, then conductivity, $\sigma =\frac{1}{\rho }$
According to definition of specific resistance
$\rho =\frac{E}{J}$,
where $E$ is intensity of electric field at a point inside conductor and $J$ is current density.
$\therefore \sigma =\frac{J}{E}$
Or $\overrightarrow{J}=\sigma \overrightarrow{E}$