The current density
(in MKS), where is the permittivity of free space and E is the electric field, having units of amps per square meter, and arising in Maxwell's generalization of Ampère's law
where B is the magnetic field, is the permeability of free space, and J is the physical current density.
The term is an important component of the Maxwell equations, and represents magnetic effects caused by varying electric fields that were unknown at Ampère's time. In a way, is a fictitious quantity, since it does not correspond to an actual current, but inclusion of this term is mandatory to successfully explain observed physical phenomena accompanying time-varying electric fields.
Ampère's Law, Current, Maxwell Equations
References
Bekefi, G. and Barrett, A. H. Electromagnetic Vibrations, Waves, and Radiation. Cambridge, MA: MIT Press, pp. 199-201, 1987.
