Induced EMF and Current in a Shrinking Loop Shrinking Loop. A circular loop of f

Question

Induced EMF and Current in a Shrinking Loop
Shrinking Loop. A circular loop of flexible iron wire has an initial circumference of 161cm , but its circumference is decreasing at a constant rate of 13.0cm/s due to a tangential pull on the wire. The loop is in a constant uniform magnetic field of magnitude 1.00T , 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.




Part A
Find the magnitude of the emf EMF induced in the loop after exactly time 8.00s has passed since the circumference of the loop started to decrease.

I have tried to follow 2 examples on this site and can't get it. Can you please help me? Thanks

Explanation / Answer

E = d/dt so we need an expression for . = BA = Br2 and since circumference C = 2r, we can write that as = BA = B(C2/42) = BC2/4

Therefore d/dt = (BC/2) (dC/dt) since we know C is a function of t.

We also know that after 8 seconds, the circumference is 161 - 8*13 = 57 cm.

= (1.00 T)(0.57 m/2)(0.13 m/s)

0.0118 V

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