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[103 ]m 2 (0.500T )377 rad
s