nLab Ohm's law

Selected writings

In electromagnetism, Ohm’s law states that, in an electric conductor, the electric current $\vec J$ is proportional to the electric field $\vec E$. This linear relationship is encoded by a matrix called the resistivity tensor $\rho$

$$\vec E \,=\, \rho \cdot \vec J \,,$$

or equivalently by its inverse matrix, called the conductivity tensor $\sigma$

$$\vec J \,=\, \sigma \cdot \vec E \,.$$

Related entries

• Hall effect, quantum Hall effect

Literature

See also:

• Wikipedia: Ohm’s law