Biomedical Engineering Reference
In-Depth Information
F
1
QQ
1
Q
E
==
ch
1
=
ch
(3.28)
2
2
q
4
πε
Qr
4
πε
r
0
1
0
The electric field strength in a given region is also referred by the electrical flux,
similar to molar flux. Electrical flux is the number of electrical field lines per unit
area. The electric field from any number of point charges is obtained from a vec-
tor sum of the individual fields [Figure 3.6(c)]. A positive charge is taken to be an
outward field and negative charge to be an inward field.
Work is defined as the component of force in the direction of motion of an
object times the magnitude of the displacement of the object
g
WFd
=
⊥
For example, if a box is moving in the horizontal direction across the floor, the
work done by the force
F
is
F
cos
(Figure 5.2) times the magnitude of the displace-
ment traveled,
d
, across the floor. Work done by gravitation force is independent
of the path and the work done by that force is written as the negative of a change
in potential energy, that is,
θ
(
)
WPEPE
=−
−
g
f
i
where
PE
f
is the final potential energy and
PE
i
is the initial potential energy. In the
gravitational field, objects naturally move from high potential energy to low po-
tential energy under the influence of the field force. On the other hand, work must
be done by an external force to move an object from low potential energy to high
potential energy. Similarly, to move a charge in an electric field against its natural
direction of motion would require work. The exertion of work by an external force
would in turn add potential energy to the object. Work done by electrical force can
also be written, similar to gravitational field, as
(
)
WPEPE
=−
−
E
f
i
The work done by the electric force when an object
Q
1
is moved from point
a
to point
b
in a constant electric field is given by
E
WQE d
=
cos
θ
1
where
d
is the distance between the final position and the initial position, and cosq
is the angle between the electric field and the direction of motion. This work would
change the potential energy by an amount which is equal to the amount of work
done. Thus, the electric potential energy is dependent upon the amount of charge on
the object experiencing the field and upon the location within the field.
