Biomedical Engineering Reference
In-Depth Information
The electric field is a vector quantity whose direction is defined, by convention, as
the direction that a positive test charge would be pushed in when placed in the field.
Thus, the electric field direction about a positive source charge is always directed
away from the source, and the electric field direction about a negative source charge
is always directed toward the source [Figure 3.6(a)].
A charged object can have an attractive effect upon an oppositely charged ob-
ject or a repulsive effect upon the same charged object even when they are not in
contact. This phenomenon is explained by the electric force acting over the dis-
tance separating the two objects. Consider the electric field created by a positively
charged (
Q
) sphere [Figure 3.6(b)]. If another positive charge
Q
1
enters the electri-
cal field of
Q
, a repulsive force is experienced by that charge. According to
Cou-
lomb's law
, the amount of electric force is dependent upon the amount of charge
and the distance from the source (or the location within the electrical field). The
electric force (
F
E
) acting on a point charge
Q
ch
as a result of the presence of a sec-
ond point charge
Q
1
is given by
kQ Q
(3.27)
F
=
C h
1
E
2
r
where
k
C
is the Coulomb's law proportionality constant. The units on
k
C
are such
that when substituted into the equation the units on charge (coulombs) and the
units on distance (meters) will be canceled, leaving a Newton as the unit of force.
The value of
k
C
is dependent upon the medium that the charged objects are im-
mersed in. For air,
k
C
is approximately 9
10
9
Nm
2
/C
2
. For water,
k
C
reduces by as
much as a factor of 80.
k
C
is also related to permittivity (
×
ε
0
) of the medium by the
1
relation
k
=
and normally Coulomb's law with permittivity is used.
4
πε
0
If two objects of different charges, with one being twice the charge of the other,
are moved the same distance into the electric field, then the object with twice the
charge requires twice the force. The charge that is used to measure the electric field
strength is referred to as a test charge since it is used to
test
the field strength. The
magnitude of the electric field or electrical field strength
E
is defined as the force
per charge of the test charge.
Figure 3.6
Electric fi eld: (a) convention of direction; (b) infl uence of point source; and (c) multiple
point charges.
