Problem 19

  The drawing shows a straight wire, a part of which is bent into the shape of a circle. The radius of the circle is 2.0 cm. A constant magnetic field of magnitude 0.55 T is directed perpendicular to the plane of the paper. Someone grabs the ends of the wire and pulls it taut, so the radius of the circle shrinks to zero in a time of 0.25 s. Find the magnitude of the average induced emf between the ends of the wire.

SOLUTION: The average emf induced in the circular wire is given by

$$emf = -B\left (\frac{A - A_o}{t - t_o} \right ) \cos\phi$$

Again, $\cos\phi = 1$, so that (noting that the minus signs cancel)

$$emf = (0.55 T)\left [\frac{\pi(2 \times 10^{-2} m)^2}{0.25 s}\right ]$$

$$emf = 2.8 \times 10^{-3} V$$