Electromagnetic Force

The basic principle of motor action is the so called
electromagnetic force or Lorentz force production.

Lorentz force states that "when a current carrying conductor is
placed in a magnetic field, it is subject to a force which we call
Lorentz force ".

The magnitude of the force depends upon the orientation of the
conductor with respect to the direction of the field. The force is
greatest when the conductor is perpendicular to the field and zero
when it is parallel to it. Between these two extremes, the force has
intermediate values.
The maximum force acting on a straight conductor is given by

F = Bli

Where F : Is the force acting on the conductor (N),
B : Is the flux density of the field (T), and,
l : Is the length of the conductor facing the magnetic field(m).
i: the current in the conductor (A).

The direction of the magnetic force can be determined by using
Felming left hand rule. Before going to show this rule, it is better to
explain the physical meaning of the lorentz force. This can be easly
explaind by with the help of the following two figures (Fig. And
Fig. ). For a current flowing into the page of this book, the circular
lines of force have the direction shown in Figure 2.32a. The same
figure shows the magnetic field created between the N, S poles of a
powerful permanent magnet.

The magnetic field does not, of course, have the shape shown in
the figure because lines of force never cross each other. What,
then, is the shape of the resulting field?. To answer the question,
we observe that the lines of force created respectively by the
conductor and the permanent magnet act in the same direction
above the conductor and in opposite directions below it.
Consequently, the number of lines above the conductor must be
greater than the number below. The resulting magnetic field
therefore has the shape given in Figure 2.32b.

Recalling that lines of flux act like stretched elastic bands, it is
easy to visualize that a force acts upon the conductor, tending to
push it downward.

Now let us Define Felmeng left hand rule It is illustrated in Fig.
6-9.

The direction of the force can also be determined by using the
right-hand screw rule, illustrated in Fig.2.2(b).
Turn the current vector i toward the flux vector B. If a screw is
turned in the same way, the direction in which the screw will move
represents the direction of the force f.

Note that in both cases (i.e., determining the polarity of the
induced voltage and determining the direction of the force) the
moving quantities (v and i ) are turned toward B to obtain the
screw movement.
Equations (2.1) and (2.2) can be used to determine the induced
voltage and the electromagnetic force or torque in an electric
machine. There are, of course, other methods by which these
quantities (e and f) can be determined.

Source ( pdf )
http://faculty.ksu.edu.sa/eltamaly/Documents/Courses/EE%20339/

MAGNETIC%20CIRCUITS.pdf

Electromagnetic Force, f

For the current-carrying conductor shown in Fig.3.3(a), the
force (known as Lorentz force) produced on the conductor can be
determined from the following equation:

f = Bli (3.2)

where B, l, and i are mutually perpendicular. The direction of
the force can be determined by using the Fleming’s Left Hand Rule
or right-hand screw rule as explaind in the previous chapter and
are stated in the following. The direction of the force is illustrated
in Fig.3.3(b).

Fleming’s Left Hand Rule:
“Hold out your left hand with forefinger, second finger and thumb
at right angles to one another. If the forefinger represents the
direction of the field, and the second finger that of the current, then
thumb gives the direction of the motion or force.”


Right-Hand Screw Rule:
Turn the current vector i toward the flux vector B. If a screw is
turned in the same way, the direction in which the screw will move
represents the direction of the force f.
Note that in both cases (i.e., determining the polarity of the
induced voltage and determining the direction of the force) the
moving quantities (v and i ) are turned toward B to obtain the
screw movement.

Equations (3.1) and (3.2) can be used to determine the induced
voltage and the electromagnetic force or torque in an electric
machine. There are, of course, other methods by which these
quantities (e and f) can be determined.

Source ( pdf )
http://faculty.ksu.edu.sa/eltamaly/Documents/Courses/EE%20339/

DC%20Machines2.pdf