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 167cm , but its circumference is decreasing at a constant rate of 10.0cm/s due to a tangential pull on the wire. The loop is in a constant uniform magnetic field of magnitude 0.600T , 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 E induced in the loop after exactly time 2.00s has passed since the circumference of the loop started to decrease.

Express your answer numerically in volts to three significant figures.

Explanation / Answer

Here ,

rate of decrease of circumference , dC/dt = 10 cm/s

Now , as dr/dt = dC/dt /2pi

dr/dt = 10/2pi cm/s

dr/dt = 1.592 cm/s

NOw, initial r0 = C0/2pi

r0 = 167/2pi

r0 = 26.6 cm

after 2 sec ,

r = 26.6 - 2 * 1.592

r = 23.4 cm

>> induced emf = rate of change of flux

induced emf = B*dA/dt

induced emf = B* d/dt(pi*r^2)

induced emf = 2pi*B*r * dr/dt

induced emf = 2pi*0.6 * 0.234 *0.01592

induced emf = 0.014 V

the induced emf is 0.014 V

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