Page 57 - Electric Machinery Fundamentals

lNTRODUCTlON TO MACHINERY PRlNCIPLES 33

X x x X B
I
X X X X
X X X X

X X X X
F
X X X X
X X X X FIGURE 1- 16
A current-carrying wire in the presence of a
X X X X magnetic field.

1.6 PRODUCTION OF INDUCED FORCE
ON AWIRE
A second major effect of a magnetic field on its surroundings is that it induces a force
on a cun'ent-calTying wire within the field. The basic concept involved is illustrated
in Figure 1-16. The figure shows a conductor present in a unifonn magnetic field of
flux density B, pointing into the page. The conductor itself is I meters long and con-
tains a CUlTent of i amperes. The force induced on the conductor is given by
F = ;(1 X B) (1-43)
where
i = magnitude of current in wire
I = length of wire, with direction of I defined to be in the direction of
current flow
B = magnetic flux density vector
The direction of the force is given by the right-hand rule: If the index finger of the
right hand points in the direction of the vector I and the middle finger points in the
direction of the flux density vector B, then the thumb points in the direction of
the resultant force on the wire. The magnitude of the force is given by the equation
F = itB sin e (1-44)
where e is the angle between the wire and the flux density vector.

Example 1-7. Figure 1-16 shows a wire carrying a current in the presence of a
magnetic field. The magnetic flux density is 0.25 T, directed into the page. If the wire is
1.0 m long and carries 0.5 A of cutTent in the direction from the top of the page to the bot-
tom of the page, what are the magnitude and direction of the force induced on the wire?
(
Solution
The direction of the force is given by the right-hand rule as being to the right. The magni-
tude is given by
F = itB sin e (1-44)
~ (0.5 A)(l.O m)(0.25 T) sin 90 0 = 0.125 N