Page 58 - Electric Machinery Fundamentals

34 ELECTRJC MACHINERY FUNDAMENTALS

Therefore,
F = 0.125 N, directed to the right

The induction of a force in a wire by a cun-ent in the presence of a magnetic
field is the basis of motor action. Almost every type of motor depends on this
basic principle for the forces and torques which make it move.
1.7 INDUCED VOLTAGE ON A CONDUCTOR
MOVING IN A MAGNETIC FIELD
There is a third major way in which a magnetic field interacts with its surround-
ings. If a wire with the proper orientation moves through a magnetic field, a volt-
age is induced in it. This idea is shown in Figure 1-17. The voltage induced in the
wire is given by
eiod = (v X B) • 1 (1-45)

where
v = velocity of the wire
B = magnetic flux density vector
I = length of conductor in the magnetic field
Vector I points along the direction of the wire toward the end making the smallest
angle with respect to the vector v X B. The voltage in the wire will be built up so
that the positive end is in the direction of the vector v X B. The following exam-
ples illustrate this concept.
Example 1- 8. Figure 1- 17 shows a conductor moving with a velocity of 5.0 m/s
to the right in the presence of a magnetic field. The flux density is 0.5 T into the page, and
the wire is 1.0 m in length, oriented as shown. What are the magnitude and polarity of the
resulting induced voltage?
Solution
The direction of the quantity v X B in this example is up. Therefore, the voltage on the con-
ductor will be built up positive at the top with respect to the bottom of the wire. The direc-
tion of vector I is up, so that it makes the smallest angle with respect to the vector v X B.
Since v is perpendicular to B and since v X B is parallel to I, the magnitude of the
induced voltage reduces to
eind = (v X B) -I (1-4S)
= (vB sin 900) I cos 0°
= vBI
~ (S.O mls)(O.S T)(1.0 m)
~ 2.SV
Thus the induced voltage is 2.5 V, positive at the top of the wire.
(
Example 1- 9. Figure 1-18 shows a conductor moving with a velocity of 10 m/s
to the right in a magnetic field. The flux density is 0.5 T, out of the page, and the wire is
1.0 m in length, oriented as shown. What are the magnitude and polffi"ity of the resulting
induced voltage?