Problem 16

  A rectangular loop of wire is moving toward the bottom of the page with a speed of 0.020 m/s (see drawing). The loop is leaving a region in which a 2.4-T magnetic field exists; the magnetic field outside this region is zero. During a time of 2.0 s, what is the magnitude of the change in the magnetic flux?

SOLUTION: The change in flux is

$$\Delta\Phi = B \Delta A \cos\phi$$

The angle $\phi = 0^o$, so $\cos\phi$ = 1. The area that leaves the loop in time $\Delta$ t is the product of the width = 0.080 m and the length = v $\Delta$ t, so that

$$\Delta A = (0.080 m)(0.02 m/s)(2 s)$$

and

$$\Delta\Phi = 7.7 \times 10^{-3} Wb$$