Shrinking Loop. A circular loop of flexible iron wire has an initial circumferen

Question

Shrinking Loop. A circular loop of flexible iron wire has an initial circumference of 160 , but its circumference is decreasing at a constant rate of 14.0 due to a tangential pull on the wire. The loop is in a constant uniform magnetic field of magnitude 0.500 , which is oriented perpendicular to the plane of the loop. Assume that you are facing the loop and that the magnetic field points into the loop.
Find the magnitude of the emf induced in the loop after exactly time 6.00 has passed since the circumference of the loop started to decrease.
Find the direction of the induced current in the loop as viewed looking along the direction of the magnetic field.

Explanation / Answer

=BA
d/dt=B*dA/dt
c=2r so A=r2 ( c is circumference)
r=c/2 so A=c2/4
dA/dt=d/dt(c2/4)= (2c/4)dc/dt
d/dt= B(c/2)dc/dt
Where B=0.5
dc/dt=0.14 m/s
At 6s, c=1.6-0.14*(6s)=0.76 m
d/dt=8.47 x 10-3 V
Since F is decreasing, the EMF is positive. Since EMF positive, point thumb along A and look at fingers.
They curl counterclockwise.

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