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, Eric Weisstein's World of Math and in MKS by
Bound Current Density, Charge Density, Current, Displacement Current, Ohm's Law, Surface Current
References
Griffiths, D. J. Introduction to Electrodynamics, 3rd ed. Englewood Cliffs, NJ: Prentice-Hall, 1998.
