Page 625 - Mechatronics with Experiments

ELECTRIC ACTUATORS: MOTOR AND DRIVE TECHNOLOGY 611

E (s)
E S E
F = q E
r r
1 3
+q –q q+ r 2 e 3 q
1
e
1
e 2 q– 3
q+
2 (c)
(b)
(a)

E E
B

q
net
ds
A
dA
(d) (e)
FIGURE 8.5: Electric fields due to stationary electric charges. (a) By convention, electric fields
are assumed to eminate from positive charges and terminate at the negative charges.
(b) Electric field at a point in space due to charged particles at other locations. (c) Force acting
on a charged particle due to an electric field. (d) Integral of electric field over a closed surface is
proportional to the net charge inside the volume spanned by the closed surface. (e) Voltage
between two points in space (A and B) is equal to the line integral of electric field between the
two points.

away from the charge. The Coulomb constant is closely related to another well known
constant as follows,
1
k = (8.28)
e
4 ⋅ ⋅
o
2
2
where = 8.8542 × 10 −12 C ∕N ⋅ m is the permittivity of free space.
o
Force ( ⃗ F) exerted on a charge (q) which is in an electric field ( ⃗ E) is (Figure 8.5c)
⃗ F = q ⋅ ⃗ E (8.29)
and if the charge is free to move, the resulting motion is governed by
⃗ F = m ⋅ ⃗ a (8.30)
q
where the generated force results in the acceleration (⃗ a) of the charge mass (m ) based on
q
Newton’s second law. This last equation is used to study the motion of charged particles
in electric fields, that is the motion of electrons in cathode ray tube (CRT), or the motion
of charged small droplets in ink-jet printing machines. The motion trajectory of a particle
of a known mass can be controlled by controlling the force acting on it. The force can be
controlled either by controlling its charge or the electric field in which it travels. Generally,
the electric field is kept constant, and the charge on each particle is controlled before it
enters the electric field. Another electric field quantity of interest is the electric flux, Φ ,
E