Fundamentals of Electromagnetics - RF/Microwave Interaction with Biological Tissues - page 17

A consequence of the first contribution is that the electric and magnetic
fields are linked together; hence there is a coupling between electricity and
magnetism. As a consequence of the second contribution, the electric current
can take one more form than previously known, so that one could have the
following (the electric current passing through a given area is obtained by
surface integrating the corresponding current density):

1. A convection current density , due for instance to a density of electric
charges moving in vacuum, is described by

J = r v (1.28)

conv

2. A conduction current density , due to the conductivity of some materials,
is described by a relationship based on the electric current in the
conductor:

J = s E (1.29)

cond

3. A displacement current density , due to the time variation of the electric
field, is equal to the time derivative of the displacement field (the elec-
tric current density):

∂
∂

D
t

J =

d

(1.30)

If we consider an alternate-current source feeding a capacitor formed of
two parallel plates in vacuum through an electric wire, the displacement
current ensures the continuity between the conduction current circulat-
ing in the wire and the electric phenomenon involved between the two
capacitor plates: The displacement current density, integrated over the
area of the plate and time derived, that is, multiplied by j w, is equal to
the conduction current in the wire [3, 7].
4. A source current density .

Maxwell's equations form a system of first-order equations, vector and
scalar. They are usually considered as the generalization of the former laws
describing electricity and magnetism. This is a historical point of view, usually
accompanied by the comment that up to now no EM phenomenon has been
pointed out which does not satisfy Maxwell's equations. It has been demon-
strated, however, that Maxwell's equations can be derived from a relativistic
transformation of Coulomb law, under the constraint of the speed of light
constant with respect to the observer. The demonstration is not too difficult
in the case of linear motion, because then special relativity may be used
[1-3]. It involves, however, a significant amount of vector calculus. In the
case of rotation, however, general relativity must be used, which makes the