Image Processing Reference
In-Depth Information
It is important to recall that ρ
ν
; the electric charge density (C/m
2
) and
J
the
electric current density (A/m
2
) are sources that can induce electromagnetic
fields or be induced by the fields
Fundamentally, we can say that materials are composed of charged par-
ticles, which are displaced by the applied fields, which in turn modify the
propagation of these fields To describe this at the microscale (unit: atom, mol-
ecule, etc.), we need to define the polarizabilities, or equivalently, a scattering
parameter, such as a scattering cross section, which will be introduced later.
At the macroscale (i.e., bulk material), we introduce the constitutive param-
eters we see above:
ε: dielectric permittivity, a measure of how well a material can store
energy imposed by an electric field; it is indirectly associated with
capacitance.
μ: permeability, a measure of how efficiently energy is stored from an
applied magnetic field; it is indirectly associated with inductance.
σ: conductivity, the quantity arising from free charges that lead to cur-
rents in the presence of an applied field
where
D
()
t
=ε
()*()
t
E
t
(3.9)
B
()
t
=µ
()*()
t
H
t
(3.10)
J
()
t
=σ
()*()
t
E
t
(3.11)
3.1.3 effective permittivity and Conducting Medium
Using the above identities, we can write
J
+
j
ωε
E
≡
j
ωε
eff
E
(3.12)
where
σ
ω τ
1
ε
E
=+
+
ε
0
since
J
=
σ
E
(3.13)
1
j
j
Likewise
σ
Ne
m
2
τ
σ
=
0
and
σ
=
(3.14)
1
j
0
+
ωτ
The following simplifications are now evident:
1. At low frequencies this simplifies to
j
σ
ω
eff
=−
�
-
‚
ε
ε
0
(3.15)
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