Question

Shrinking Loop. A circular loop of flexible iron wire has an initial circumference of 167 cm , but its circumference is decreasing at a constant rate of 14.0 cm/s due to a tangential pull on the wire. The loop is in a constant uniform magnetic field of magnitude 0.900 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.

Find the magnitude of the emf E induced in the loop after exactly time 9.00 s has passed since the circumference of the loop started to decrease. Express your answer numerically in volts to three significant figures.

Answer 1

The emf induced in a wire loop is given by

where is the magnetic flux

at this case constant and perpendicular to the loop plane. A is the area of the loop given by

time variation of area is calculated as

Circumference is described by

and variation of circumference is given by the time derivative of it

or

sustituying in the area derivative we have

or

then the emf is

at t = 9 s the loop circumference length is

C=167 cm-(14cm/sec*9sec)

C=41 cm

then, finally the emf is

=-(0.90T)*0.41m/2*3.142 *(0.14m/sec)

=-0.08115786 V