# Dictionary:Conduction current

Electrical current resulting from the motion of free charges under the influence of an electric field. The density of conduction current J at a point in an isotropic medium is ${\displaystyle {\textbf {J}}=\sigma {\textbf {E}}}$, where ${\displaystyle \sigma }$ is the conductivity and E is the electric field. Conduction currents usually are more important than displacement currents in electromagnetic prospecting, depending on the frequency range. Since in general J and E are vectors, the conductivity ${\displaystyle \sigma }$ is a symmetric tensor given in Cartesian coordinates by
${\displaystyle \sigma ={\begin{vmatrix}\sigma _{xx}&\sigma _{xy}&\sigma _{xz}\\\sigma _{xy}&\sigma _{yy}&\sigma _{yz}\\\sigma _{xz}&\sigma _{yz}&\sigma _{zz}\end{vmatrix}}}$.
If one of the coordinates is in the direction of maximum conductivity and one in the direction of minimum conductivity, nondiagonal elements vanish. In isotropic materials ${\displaystyle \sigma _{xx}=\sigma _{yy}=\sigma _{zz}}$.