Page 37 - Electromagnetics

induction (although he described B as a density of lines of magnetic force). Maxwell
also included a quantity designated electromagnetic momentum as an integral part of his
theory. We now know this as the vector potential A which is not generally included as a
part of the electromagnetics postulate.
Many authors follow the original terminology of Maxwell, with some slight modifica-
tions. For instance, Stratton [187] calls E the electric field intensity, H the magnetic
field intensity, D the electric displacement, and B the magnetic induction. Jackson [91]
calls E the electric field, H the magnetic field, D the displacement, and B the magnetic
induction.
Other authors choose freely among combinations of these terms. For instance, Kong
[101] calls E the electric field strength, H the magnetic field strength, B the magnetic flux
density, and D the electric displacement. We do not wish to inject further confusion into
the issue of nomenclature; still, we find it helpful to use as simple a naming system as
possible. We shall refer to E as the electric field, H as the magnetic field, D as the electric
flux density and B as the magnetic flux density. When we use the term electromagnetic
field we imply the entire set of field vectors (E, D, B, H) used in Maxwell’s theory.

Invariance of Maxwell’s equations. Maxwell’s differential equations are valid for
any system in uniform relative motion with respect to the laboratory frame of reference in
which we normally do our measurements. The field equations describe the relationships
between the source and mediating fields within that frame of reference. This property
was first proposed for moving material media by Minkowski in 1908 (using the term
covariance) [130]. For this reason, Maxwell’s equations expressed in the form (2.1)–(2.2)
are referred to as the Minkowski form.

2.1.2 Connection to mechanics

Our postulate must include a connection between the abstract quantities of charge and
field and a measurable physical quantity. A convenient means of linking electromagnetics
to other classical theories is through mechanics. We postulate that charges experience
mechanical forces given by the Lorentz force equation. If a small volume element dV
contains a total charge ρ dV , then the force experienced by that charge when moving at
velocity v in an electromagnetic field is

dF = ρ dV E + ρv dV × B. (2.6)

As with any postulate, we verify this equation through experiment. Note that we write
the Lorentz force in terms of charge ρ dV , rather than charge density ρ, since charge is
an invariant quantity under a Lorentz transformation.
The important links between the electromagnetic fields and energy and momentum
must also be postulated. We postulate that the quantity

S em = E × H (2.7)

represents the transport density of electromagnetic power, and that the quantity

g em = D × B (2.8)

represents the transport density of electromagnetic momentum.

© 2001 by CRC Press LLC