ABSTRACT
Early studies of the properties of electric and magnetic fields, their
interplay and the resulting emission of radiation, led to formation
of several fundamental laws by Carl F. Gauss (1777-1855), Michael
Faraday (1791-1867), Andre´ M. Ampe`re (1775-1836), and James
C. Maxwell (1831-1879). These were presented in a compact
differential formalism by Maxwell (1865), which are referred to as
Maxwell’s equations:
∇ · D(r, t) = ρ(r, t), (1.1) ∇ · B(r, t) = 0, (1.2) ∇ × E(r, t) = −∂B(r, t)
∂t , (1.3)
∇ × H(r, t) = J(r, t)+ ∂D(r, t) ∂t
. (1.4)
The electric E(r, t) and the magnetic fields B(r, t), are time dependent and can be specified at every point in space and time, in
which r(= x , y, z) denotes the position vector, t is the time, J = σE, the electric current density, q(= 1.6 × 10−19 C) the elementary charge, E and B, the electric field strength and the magnetic induction, respectively, H = B/μ, the magnetic field, D = E, the
electric displacement, ρ, the volume density of free charge, , μ, and
σ the respective dielectric permittivity, the magnetic permeability,
and conductivity of the medium, “×,” the cross product, and
∇ = i ∂ ∂x
+ j ∂ ∂y
+ k ∂ ∂z . (1.5)
represents a linear vector differential operator.