Image Processing Reference
InDepth 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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