Image Processing Reference
InDepth 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 timedependent Maxwell's equations
Let us list the timedependent 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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