Page 578 - Engineering Electromagnetics, 8th Edition

560 ENGINEERING ELECTROMAGNETICS

Table B.1 (Continued)
Symbol Name Unit Abbreviation
ω Radian frequency radian/second rad/s
c Velocity of light meter/second m/s
λ Wavelength meter m
η Intrinsic impedance ohm
k Wave number meter −1 m −1
α Attenuation constant neper/meter Np/m
β Phase constant radian/meter rad/m
f Frequency hertz Hz
S Poynting vector watt/meter 2 W/m 2
P Power watt W
δ Skin depth meter m
Reflection coefficient
s Standing wave ratio
γ Propagation constant meter −1 m −1
G Conductance siemen S
Z Impedance ohm
Y Admittance siemen S
Q Quality factor

Finally, other systems of units have been used in electricity and magnetism. In the
electrostatic system of units (esu), Coulomb’s law is written for free space,
Q 1 Q 2
F = (esu)
R 2
The permittivity of free space is assigned the value of unity. The gram and centimeter
are the fundamental units of mass and distance, and the esu system is therefore a cgs
system. Units bearing the prefix stat- belong to the electrostatic system of units.
In a similar manner, the electromagnetic system of units (emu) is based on
Coulomb’s law for magnetic poles, and the permeability of free space is unity. The
prefix ab- identifies emu units. When electric quantities are expressed in esu units,
magnetic quantities are expressed in emu units, and both appear in the same equa-
tion (such as Maxwell’s curl equations), the velocity of light appears explicitly. This
2
2
follows from noting that in esu 0 = 1, but µ 0 0 = 1/c , and therefore µ 0 = 1/c ,
2
and in emu µ 0 = 1, and hence 0 = 1/c . Thus, in this intermixed system known as
the Gaussian system of units,
1 ∂D
∇× H = 4πJ + (Gaussian)
c ∂t
Other systems include the factor 4π explicitly in Coulomb’s law, and it then does
not appear in Maxwell’s equations. When this is done, the system is said to be rational-
ized. Hence the Gaussian system is an unrationalized cgs system (when rationalized
it is known as the Heaviside–Lorentz system), and the International System we have
used throughout this book is a rationalized mks system.