Lecture
From the system of Maxwell's equations it follows that sources of electromagnetic fields can be electric currents and charges.
When considering Maxwell's equations, the symbol 
denoted the conduction current density in a medium, which is related to the existence of an electric field by the constitutive equation 
. In addition to this
current, other currents may exist in any given region of space, which should be regarded as the primary cause of the appearance of an EMF,
and which can be taken as given when calculating fields. These currents are conventionally
called extraneous (external). Such currents usually include galvanic
currents, currents of exciting generators, or currents from devices
replacing such generators. To denote the density of extraneous currents
the symbol 
is usually used. The first Maxwell equation, taking into account
extraneous currents, is written as:
as:
. (2.16)
Similarly, we can introduce extraneous fields ext E
, (2.17)
or extraneous charges
(2.18)
Note that in the case of time-varying fields, the extraneous currents and extraneous charges must be related by the continuity equation
. (2.19)
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