Biomedical Engineering Reference
In-Depth Information
1.4 Electric Field
Suppose now we have a point charge
Q
at the coordinate origin, and we place another point
charge
q
at point P that has position vector
r
(Figure 1.3).
q
r
Q
Origin
Figure 1.3
Field concept
The force exerted by
Q
on
q
is
1
4πε
0
Qq
r
3
r
=
F
which I can rewrite trivially as
r
3
r
q
The point is that the term in brackets is to do with
Q
and the vector
r
, and contains no
mention of
q
. If we want to find the force on any arbitrary
q
at
r
, we calculate the quantity
in brackets once and then multiply by
q
. One way of thinking about this is to imagine that
the charge
Q
creates a certain field at point
r
, which determines the force on any other
q
when placed at position
r
.
This property is called the
electric field
E
at that point. It is a vector quantity, like force,
and the relationship is
1
4πε
0
Q
F
=
F
(on
q
at
r
)
=
q
E
(at
r
)
Comparison with Coulomb's law, Equation (1.3), shows that the electric field at point
r
due
to a point charge
Q
at the coordinate origin is
1
4πε
0
Q
r
r
3
E
=
(1.5)
E
is sometimes written
E
(
r
) to emphasize that the electric field depends on the position
vector
r
.
Electric fields are vector fields and they are often visualized as
field lines
. These are
drawn such that their spacing is inversely proportional to the strength of the field, and their
tangent is in the direction of the field. They start at positive charges and end at negative
charges, and two simple examples are shown in Figure 1.4. Here the choice of eight lines
is quite arbitrary.
Electric fields that do not vary with time are called
electrostatic
fields.
