velocity in vacuum that is measured in a unit of [m/s]. Notice also that the light
velocity c in vacuum is defined as
c ¼ 299 792 458 m=s
½
Š exact number
ð
Þ :
Thus, we have
e c ¼ 299 792 458 dimensionless number
ð
Þ :
Vacuum is a kind of dielectric media. From (7.8), its dielectric constant ε 0 is
defined by
ε 0 ¼
10
7
4πe c
2
C
2
Nm
2
!
% 8:854 Â 10
À12
C
2
Nm
2
!
:
ð7:9Þ
Meanwhile, 1 s (second) has been defined from a certain spectral line emitted from
133 Cs. Thus, 1 m (meter) is defined by
distance along which light is propagated in vacuum during 1 s
ð
Þ =299 792 458:
The quantity B is called magnetic flux density [
VÁs
m 2 ¼
Wb
m 2 ]. Equation (7.2) represents Gauss’s law of magnetostatics. In contrast to (7.1), RHS of (7.2) is zero. This
corresponds to the fact that although a true charge exists, a true “magnetic charge”
does not exist. (More precisely, such charge has not been detected so far.) The
quantity B is connected with magnetic field H by the following relation:
B = μH,
ð7:10Þ
where μ [
N
A
2 ] is said to be permeability (or magnetic permeability). Thus, H has a
dimension [
A
m ]. Permeability of vacuum μ 0 is defined by
μ 0 ¼ 4π=10
7 N
A
2
!
:
ð7:11Þ
Also we have
μ 0 ε 0 ¼ 1=c
2
:
ð7:12Þ
We will encounter this relation later again. Since the quantities c and ε 0 have a
defined magnitude, so does μ 0 from (7.12).
We often make an issue of a relative magnitude of dielectric constant and
magnetic permeability of a dielectric medium. That is, relative permittivity ε r and
relative permeability μ r are defined as follows:
7.1 Maxwell’s Equations and Their Characteristics
271