Biomedical Engineering Reference
In-Depth Information
the EEG are not simple point-like charge accumulations but rather are dipole-like
layers. Moreover, these layers are convoluted and enmeshed in a volume conductor
with spatially heterogeneous conductivity. The particular geometry and orientation
of these layers determines the potential distribution within or at the surface of the
3D body. Nevertheless, charged conductors, which have reached electrostatic equi-
librium [Figure 3.7(a)] follow these characteristics:
1. The charge spreads itself out when a conductor is charged.
2. The excess charge lies only at the surface of the conductor.
3. Charge accumulates, and the field is strongest on pointy parts of the
conductor.
4. The electric field at the surface of the conductor is perpendicular to the
surface.
5. The electric fi eld is zero within the solid part of the conductor.
Gauss' law of electricity
(named after Carl F. Gauss, a German physicist) is a
form of one of Maxwell's equations, the four fundamental equations for electricity
and magnetism. According to Gauss' law of electricity, for any closed surface that
surrounds a volume distribution of charge, the electric flux passing through that
surface is equivalent to the total enclosed charge. In other words, if
E
is the electric
field strength [Figure 3.7(b)] and
Q
is the total enclosed charge, then
Q
∫
EdA
•=
(3.34)
ε
0
S
where
dA
is the area of a differential square on the closed surface
S
with an outward
direction facing normal to the surface.
ε
0
, the permittivity of free space, is 8.8542
10
−12
C
2
/Nm
2
. The dot product is used to get the scalar part of
E
as the direction
is known to be perpendicular to the area. To prove the Gauss theorem, imagine a
sphere with a charge in the center. Substituting for
E
from (3.28) and denoting
dA
in spherical coordinates, for ease of use:
×
Figure 3.7
(a, b) Volume conductors.
