Image Processing Reference
In-Depth Information
Three
Scattering Fundamentals
3.1 MAteRIAl pRopeRtIeS And ModelIng
3.1.1 the Model for Conductivity
The most basic equation of motion is that given by Newton, and it describes
how a charged particle is affected by an electric field:
d
d
v
t
v
�
-
‚
=
m
+
eE
(3.1)
τ
where
m
is the electron mass,
e
its charge,
v
the velocity and
t
is time; here
we add a damping term with relaxation time τ. Throughout this topic we will
assume waves to have a temporal variation,
e
j
ω
t
(ω is the angular frequency).
From the above equation, we can now write
e
m
E
v
=
(3.2)
j
+ω()
1/
and the current density is expressed as
Ne
m
τ
E
j
2
J
=
Nev
=
(3.3)
1
+
ωτ
which, as we have already seen, can be written as
σ
Ne
m
τ
2
0
J
=
σ
E
where
σ
=
and
σ
=
(
electrical conductivity
)
(3.4)
0
1
+
j
ωτ
3.1.2 time-dependent Maxwell's equations
Let us list the time-dependent forms for Maxwell's equations:
Electric fluxdensity (units C/m)
2
D
→∇⋅
D
()
t
=
ρ
()
t
(3.5)
Electric field intensity (units V/m)
E
→∇⋅
B
()
t
=
0
(3.6)
= −
∂
∂
B
()
()
t
Magnetic fluxdensity (units W/m)
2
B
→∇×
E
()
t
(3.7)
t
+
∂
∂
D
()
()
t
Magnetic field intensity (units A/m)
H
→∇×
H
()
t
=
J
()
t
(3.8)
t
31
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