Transcript Induction
Voltage Induced in a Loop Rotating in a Constant Magnetic Field
Important points to consider:
The area vector is perpendicular to the plane of the loop.
Sketch the problem.
must be in rad/s.
Vmax occurs when sin t = 1.
Vmin occurs when sin t = 0.
Use radian mode.
The Problem:
A simple ac alternator is used to generate a peak output voltage of 24.0
V. The square armature (rotating loops) consists of windings that are
5.0 cm on a side and rotates in a magnetic field of 0.500 T at a rate of
60 rev/s. How many loops, N, of wire must be wound on the square
armature?
24.0 V
Re v 2 rad
rad
f 60
377
s Re v
s
B
(t ) NAB sin( t )
varies, with time, from 0 to 24 V as sin t varies from 0 to 1.
Here, the voltage given is peak, so sin t must equal 1.
3
A LW 0.050m(0.050m) 2.5[10 ]m
2
(t ) NAB (1)
(t )
24.0V
N
51
AB 2.5[103 ]m 2 (0.500T )377 rad
s