14.1 Basic Concepts and Formulae
635
Now the flux of current from a closed surface is the decrease of the charge inside
the surface. In general this cannot be zero because charges can be moved from one
place to another. This difficulty is avoided by adding the term ∂ D/∂t, where D =
ε 0 E, on the right-hand side of (32).
Integral Form
ϕ E =
B.ds = 0 (Gauss’ law for magnetostatics)
(14.36)
ϕ E =
E.ds =
q enc
ε 0
(Gauss’ law for electrostatics)
(14.37)
E.ds = −
dϕ B
dt
(Faraday’s law of induction)
(14.38)
B.ds = μ 0 ε 0
dϕ E
dt
+ μ 0 i enc (Ampere-Maxwell law)
(14.39)
Electromagnetic Waves
The E- and H -waves are transverse to the direction of propagation and are perpendicular to each other.
∇ × (∇ × E) = −∇
2 E + ∇(∇.E)
(14.40)
Wave Equation
∇
2 E = −ω
2
μ 0 ε 0 E
(14.41)
The Intrinsic Impedance
η =
μ
ε
(14.42a)
η 0 =
μ 0
ε 0
= 377 (free space)
(14.42b)
The Poynting vector (S) represents the power in the electromagnetic wave and is
given by
S = E × H
(14.43)
and points in the direction of propagation of the wave.
The skin thickness (δ) represents the depth to which an electromagnetic wave of
frequency f = ω/2π can penetrate a medium and is given by