Shrinking Loop A circular loop of flexible iron wire has an

Shrinking Loop. A circular loop of flexible iron wire has an initial circumference of 161 cm , but its circumference is decreasing at a constant rate of 13.0 cm/s due to a tangential pull on the wire. The loop is in a constant uniform magnetic field of magnitude 0.500 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 E induced in the loop after exactly time 8.00 s has passed since the circumference of the loop started to decrease.

Express your answer numerically in volts to three significant figures.

Solution

initial circumference , C = 161 cm

at t = 8 s

C = 161 - 13*8

C = 57 cm

let the radius as this time is r

2pi * r = C

2pi * r = 57 cm

r = 57/(2pi) cm

Now , dA/dt = d/dt(pi * r^2)

dA/dt = 2pi * r * dr/dt

dA/dt = C * dC/dt/(2pi)

dA/dt = 0.57 * 0.13/(2pi)

Now , for the induced emf

induced emf = dA/dt * magnetic field

induced emf = 0.57 * 0.13/(2pi) * 0.50

induced emf = 0.0058966 V = 5.89 mV