An electrical current flowing through a solid, and having units of charge per unit time per unit area (measured in the direction perpendicular to the flow direction). For electrons with number density flowing through a solid with velocity v, the resulting volume current J is given by

where is the charge on an electron. Experimentally, it is observed that the volume current is proportional to the applied electric field E,

where is a constant called the electrical conductivity, which is equivalent to Ohm's law.
The bound current density caused by a magnetization M is given in cgs by

where c is the speed of light and is the curl,and in MKS by