Write Ohm's law in the form of current density (vector form).

(N/A) Ohm's law in its microscopic or vector form relates the current density vector $\vec{J}$ to the electric field vector $\vec{E}$.
According to Ohm's law,the current density $\vec{J}$ at a point in a conductor is directly proportional to the electric field $\vec{E}$ at that point.
Mathematically,this is expressed as:
$\vec{J} = \sigma \vec{E}$
Where:
$\vec{J}$ is the current density vector (measured in $A/m^2$),
$\sigma$ is the electrical conductivity of the material (measured in $\Omega^{-1} m^{-1}$ or $S/m$),
$\vec{E}$ is the electric field vector (measured in $V/m$).
Alternatively,since $\sigma = 1/\rho$,where $\rho$ is the resistivity,the equation can also be written as $\vec{E} = \rho \vec{J}$.