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.