Biomedical Engineering Reference
In-Depth Information
P (t)
=
p
0
e
-1/
t
t
t
= 0
t
Time
FIGURE 4.4
Return of polarization to zero. Electric field is cut when
t
=
0.
movement is interrupted by an intermolecular binding force and is submitted
to resistance from the thermal motion. In this case, there is a time delay
associated with the motion of the permanent dipole toward the electric field
direction. Accordingly, under the condition which has produced a uniform
polarization
P
(generally a vector representation) by applying the electrostatic
field on this liquid beforehand, if the electrostatic field is suddenly shut off in
time (
t
0), it takes some time until the polarization returns to zero, as shown
in Figure 4.4. The parameter t in this figure is called
relaxation time
: It is the
time used by the polarization to decrease in
1/e
of its steady-state value. Based
on these phenomena, the relationship between polarization
P
and electrostatic
field
E
is shown by the following equation:
=
(
)
pE
S
=
ee
0
-
1
C m
2
-
(4.1)
E
0
e
jwt
is applied to
dielectric material exhibition relaxation, the polarization
P
has a phase delay
with respect to the applied electric field. Therefore,
complex permittivity
has
been introduced as the way for expressing the delay of this polarization. There-
fore, the dielectric constant is expressed as a complex permittivity. By denot-
ing the complex permittivity e
As mentioned above, when an alternating electric field
E
=
.
s
j
e
s
, the expression related to Eqn. (4.1)
when applying alternating electric field
E
=
e
s
-
E
0
e
j
w
t
is described by the equation
=
˙
()=
(
˙
)
pt
ee
-
1
Ee
jt
w
(4.2)
0
S
0
V
0
e
j
w
t
is applied to the dielectric material
by a parallel-plate applicator, as shown in Figure 4.5, the electric power loss
W
absorbed in the dielectric is calculated using the complex permittivity. As
When the alternating voltage
V
=
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