Page 128 - Electromagnetics

Figure 3.1: Positive point charge in the vicinity of an insulated, uncharged conductor.

It is important to note that any separation of the electromagnetic field into independent
static electric and magnetic portions is illusory. As we mentioned in § 2.3.2, the electric
and magnetic components of the EM field depend on the motion of the observer. An
observer stationary with respect to a single charge measures only a static electric field,
while an observer in uniform motion with respect to the charge measures both electric
and magnetic fields.

3.1.2 Static field equilibrium and conductors

Suppose we could arrange a group of electric charges into a static configuration in free
space. The charges would produce an electric field, resulting in a force on the distribution
via the Lorentz force law, and hence would begin to move. Regardless of how we arrange
the charges they cannot maintain their original static configuration without the help
of some mechanical force to counterbalance the electrical force. This is a statement of
Earnshaw’s theorem, discussed in detail in § 3.4.2.
The situation is similar for charges within and on electric conductors. A conductor
is a material having many charges free to move under external influences, both electric
and non-electric. In a metallic conductor, electrons move against a background lattice
of positive charges. An uncharged conductor is neutral: the amount of negative charge
carried by the electrons is equal to the positive charge in the background lattice. The
distribution of charges in an uncharged conductor is such that the macroscopic electric
field is zero inside and outside the conductor. When the conductor is exposed to an addi-
tional electric field, the electrons move under the influence of the Lorentz force, creating
a conduction current. Rather than accelerating indefinitely, conduction electrons experi-
ence collisions with the lattice, thereby giving up their kinetic energy. Macroscopically,
the charge motion can be described in terms of a time-average velocity, hence a macro-
scopic current density can be assigned to the density of moving charge. The relationship
between the applied, or “impressed,” field and the resulting current density is given by
Ohm’s law; in a linear, isotropic, nondispersive material this is

J(r, t) = σ(r)E(r, t). (3.21)

The conductivity σ describes the impediment to charge motion through the lattice: the

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