Direct Energy, 2018a

16 1.6 Electromagnetic Waves
−→ A
H (x, y, z, t)=Magnetic eld intensity in
m
−→ Wb
B (x, y, z, t)=Magnetic ux density in
m 2
In these expressions,V represents the units volts,C represents the units
coulombs,A represents the units amperes,and Wb represents the units
webers. Additional abbreviations for units are listed in Appendix B.
Coulomb's law
−→ Q 1 Q 2 â r
F = (1.3)
4πɛr 2
tells us that charged objects exert forces on other charged objects. In this
expression, Q 1 and Q 2 are the magnitude of the charges in coulombs. The
quantity ɛ is the permittivity of the surrounding material in units farads
per meter,and it is discussed further in Sections 1.6.3 and 2.2.3. The
quantity r is the distance between the charges in meters,and â r is a unit
vector pointing along the direction between the charges. Force in newtons
is represented by −→ F . Opposite charges attract,and like charges repel.
Electric eld intensity is force per unit charge,so the electric eld intensity
due to a point charge is given by
−→ Qâ r E = (1.4)
4πɛr 2
These vector elds can describe forces on charges or currents in a circuit
as well as outside the path of a circuit. Maxwell's equations relate time
varying electric and magnetic elds. Maxwell's equations in dierential
form are:
−→ ∇×
−→ E = −
∂ −→ B
∂t
−→ ∇×
−→ H =
−→ J +
∂ −→ D
∂t
Faraday's Law (1.5)
Ampere's Law (1.6)
−→ ∇·−→ D = ρch Gauss's Law for the Electric Field (1.7)
−→ ∇·−→ B =0 Gauss's Law for the Magnetic Field (1.8)
The additional quantities in Maxwell's equations are the volume current
density −→ J in m A and the charge density ρ 2
ch in m C . In this text,we will not
3
be solving Maxwell's equations,but we will encounter references to them.