Page 340 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 27] MAGNETISM 325

2
The magnetic force Qv B in the particle provides the centripetal force mv /r that keeps it moving in a circle of
radius r. Hence
F magnetic = F centripetal
mv 2
Qv B =
r
mv
r =
QB
The radius is directly proportional to the particle’s momentum mv and inversely proportional to its charge Q and the
magnetic field B.

SOLVED PROBLEM 27.10
Show that a current-carrying wire loop experiences a torque in a magnetic field provided the plane of the
loop is not perpendicular to the field.

Figure 27-9(a) shows a current-carrying loop whose plane is parallel to a magnetic field B. Sides A and C of
the loop are parallel to B, and so no magnetic force acts on them. Sides B and D are perpendicular to B, however,
and each experiences the force shown. Since F B is opposite in direction to F D along different lines of action, they
produce a torque on the loop. Such a torque will occur even if the plane of the loop is not parallel to B, although it
will then be smaller since the moment arm will be shorter, provided the plane is not perpendicular to B.
In Fig. 27-9(b), the plane of the loop is perpendicular to B.Now F A and F C are equal and opposite along the
same line of action, as are F B and F D , so there is no net torque on the loop.

F C

F D
C
F B F = 0 D B
C
C B
D
B
B
I
A
A F
F D B
F = 0 F A
a
I
(a) (b)
Fig. 27-9

SOLVED PROBLEM 27.11
Briefly describe the operation of a simple direct-current electric motor.

Figure 27-10 shows a simple dc electric motor in which a wire loop rotates in the magnetic field of a permanent
magnet. The direction of rotation with the current as shown is clockwise. To produce continuous movement, the
current in the wire loop must be reversed when the loop is vertical. The reversed current then interacts with the
magnetic field to coninue to turn the loop clockwise through a half-turn. Now the current must be reversed again, and
so forth. The device used to automatically change the current direction is called the commutator; it is visible on the
shaft of a dc motor as a copper sleeve divided into segments. Often electromagnets rather than permanent magnets
are used to create the magnetic field, and in some motors the coil is fixed and the magnet or magnets rotate inside it.
Normally more than one loop is used to give the maximum continuous torque. Ac motors do not need commutators
because the current changes direction back and forth many times per second.