A constant magnetic field of magnitude 8.9 Tesla is directed parallel to a square loop with side 7.4 meters. The field is suddenly rotated 90 degrees, so that .049 seconds later its field is parallel to the plane of the loop. What is the magnitude of the average rate of change of flux in the loop during this time?
The area of the loop is ( 7.4 m) ^ 2 = 54.76 m ^ 2, so the initial flux, when the loop and field are perpendicular, is
After 90 degree turn, the loop will be parallel to the field, and will intercept none of the field.
The magnitude of the flux change from 487.3 T m ^ 2 to zero is
This flux change occurs in .049 seconds, so the average rate of flux change has magnitude
If a loop of area A is oriented perpendicular to a magnetic field B, the magnetic flux will be
If the field is suddenly rotated so that it is parallel to the plane, the flux will become 0 (the loop doesn't intercept any of the field when it is parallel to the field; also `theta = 90 deg in this orientation and `phi = B * A * cos(`theta) = B * A * 0 = 0).
So the change of flux will be
A flux change of -`phi in time interval `dt gives an average rate of flux change
The average rate of flux change is the average voltage that results from the flux change.
Any change of flux through an area results in a voltage around the boundary of that area. In particular the flux change computed here creates a voltage in the loop. Most commercial electrical power is generated by changing the flux in a loop of wire.
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