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 160cm , but its circumference is decreasing at a constant rate of 12.0cm/s due to a tangential pull on the wire. The loop is in a constant uniform magnetic field of magnitude 0.900T , 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 E induced in the loop after exactly time 6.00s has passed since the circumference of the loop started to decrease.

Explanation / Answer

a)C = 2?r, whence ?C/?t = 2? ?r/?t. ?C/?t = 14.0 x 10^(-2) m/sec (given), whence, ?r/?t = 12.0 x 10^(-2) m/sec / 2? = 1.91 x 10^(-2) m/sec. Further, at precisely six seconds, the circumference is 160cm - 12.0 cm/sec * 6 sec = 88 cm, so the radius at t = 6 sec is 88/2? = 14.00 cm = 14.00 x 10^(-2) cm. Per Faraday's law, the magnitude of the induced emf is the time derivative of the magnetic flux: in this case, since the magnetic field is constant and perpendicular to the loop, that reduces to just B ?A/?t. A = ?r

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