Question

Shrinking Loop. A circular loop of flexible iron wire has an initial circumference of 168 cm, but its circumference is decreasing at a constant rate of 12.0 cm/s due to a tangential pull on the wire. The loop is in a constant uniform magnetic field of magnitude 0.600 T 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 induced in the loop after exactly time 9 00 s has passed since the circumterence of the loop started to decrease Express your answer numerically in volts to three significant figures View Available Hint s) 0.0687 Submit X Incorrect; One attempt remaining: Try Again

Answer 1

Circumference, C = 2 pi r

dC/dt = 2 pi dr/dt = - 0.12 m/s

Rate of change of area, dA/dt = 2 pi dr/dt = - 0.12 r

In 9 second, C decrease by 9 x 0.12 = 1.08 m

Radius = (1.68 - 1.08) /2 pi = 0.095 m

Emf, E = 0.6 x 0.12 x 0.095 = 0.0069 V

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