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Faraday's Law produces the EMF. The law states that the induced EMF
is caused by the rate of change of the magnetic flux through the loop.
d PHI
(1) EMF = - N -----
dt
Where PHI is the magnetic flux through one loop an N is the number of
loops. In this case we have only one loop so N = 1 . The flux
through the loop is changing because the orientation of the loop with
respect to the magnetic field is changing. In the figure below the loop
(depicted as a rectangle) intercepts magnetic field lines at some time t1.
->
B
^ ^
____|_^_|_^__
\ | | | | \ time = t1
\ | | | | \
\ | | \ loop
\____________\
| \
\
Axis of rotation
At some later time t2 the loop rotates to a new position relative to
the magnetic field so that it intercepts fewer (in this example no)
field lines.
->
B
|\
^ | \ ^
| |^ \ | ^
| || \ | time = t2
| || | |
| || | |
| || | |
|\ |\ |
\ | \
\| axis of rotation
So in a time t2 - t1 the magnetic flux changes. By Faraday's law this
means a EMF is induced in the wire loop. If the loop rotates with
angular velocity w about the indicated axis of rotation then the
magnetic flux at any instant in time will be
(2) PHI = BAcos(wt)
Where B is the magnitude of the magnetic field, A is the cross
sectional area of the loop and t is time. Inserting this into (1),
with N = 1 gives
d BAcos(wt)
(3) EMF = - ----------- = BAwsin(wt)
dt
********************
* *
* EMF = BAwsin(wt) *
* *
********************
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