Biomedical Engineering Reference
In-Depth Information
Electric field
Figure 1.13
Dielectric with applied field
We relate the induced electric dipole to the volume of a differential element by
d
p
e
=
P
dτ
(1.24)
where the dielectric polarization
P
is an experimentally determined quantity.
P
can depend
on the applied field in all manner of complicated ways, but for very simple media and for
low field strengths, it turns out that
P
is directly proportional to
E
. We write
(ε
r
−
P
=
1) ε
0
E
(1.25)
where ε
r
is the relative permittivity of the dielectric. The polarization acts so as to reduce
the field inside a dielectric.
1.12 Dipole Polarizability
At the microscopic level, we concern ourselves with the various electric moments that are
induced in each atom or molecule.
Consider the simple case shown in Figure 1.14, where we apply a weak electric field
E
in
a direction parallel to amolecule's electric dipolemoment. This causes charge redistribution
and we can write
p
e
(induced)
=
p
e
(permanent)
+
α
E
(1.26)
I have distinguished between the permanent electric dipole, the one a molecule has in free
space with no fields present, from the induced dipole. I have also used the symbol α for the
dipole polarizability
.
In the general case, the field need not be weak and the induced dipole need not be in the
same direction as either the applied field or the permanent dipole moment. This is shown
in Figure 1.15. Parameter α cannot be a scalar, since the directions of the applied field and
the induced dipole need not be the same.
