Environmental Engineering Reference
In-Depth Information
Figure 4.2
A magnetized needle in a magnetic field requires a counterclockwise torque to hold it in place at
an angle
θ
.
B
I
r
I
B
I
E
V
I
L
F
L
(a)
(b)
Figure 4.3
(a) A wire carrying a current
I
and moving perpendicular to a magnetic field
B
at a speed
V
is
subject to a restraining force
F
and experiences an electric field
E
. (b) A sketch of a simple armature circuit
showing how the current loop is connected to slip rings that deliver the current to an external circuit.
The magnetic interaction that underlies the operation of an electric motor or generator is
illustrated in Figure 4.2, showing a magnetized compass needle placed in a magnetic field. The
needle seeks to align itself with the magnetic field lines, as does a compass needle in the earth's
magnetic field. If we hold the needle stationary at an angle
from the direction of the magnetic
field, we must apply a torque
T
that is equal to the product of the needle's magnetic dipole moment
M
, the strength of the magnetic field
B
, and sin
θ
. Alternatively, work can be done by the needle
if it rotates to align itself with the magnetic field, in the amount
MB
θ
, but work can be
generated only for a half revolution of the needle, at most. To make an electric motor of this
device, we must reverse the direction of the needle's magnetization every half revolution. This can
be accomplished by surrounding the needle with a coil of wire through which a current flows from
an external circuit, with the current being reversed each half revolution. The basic elements of
both motor and generator are a magnetizable rotor and a stationary magnetic field, either or both
of which are connected to external electric circuits that adjust the amount and direction of the
magnetic fields.
The physical principles underlying both the electric motor and electric generator are illustrated
in Figure 4.3(a). A wire of length
L
carrying a current
I
in the presence of a magnetic field
B
is
(
1
−
cos
θ)
