chapter  1
Properties of Radiation
Pages 78

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.