Dictionary:Conduction current

{{#category_index:C|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 ${\textbf {J}}=\sigma {\textbf {E}}$, where $\sigma$ 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 $\sigma$ is a symmetric tensor given in Cartesian coordinates by

$\sigma ={\begin{vmatrix}\sigma _{xx}&\sigma _{xy}&\sigma _{xz}\\\sigma _{xy}&\sigma _{yy}&\sigma _{yz}\\\sigma _{xz}&\sigma _{yz}&\sigma _{zz}\end{vmatrix}}$.

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 $\sigma _{xx}=\sigma _{yy}=\sigma _{zz}$.