Chapter 30, Problem 56EAP

Your camping buddy has an idea for a light to go inside your tent. He happens to have a powerful (and heavy!) horseshoe magnet that he bought at a surplus store. This magnet creates a $0.\text{2}0\text{ T}$ field between two pole tips $\text{1}0\text{ cm}$ apart. His idea is to build the hand-cranked generator shown in FIGURE P30.56. He thinks you can make enough current to fully light a $\text{1}.0\Omega$ lightbulb rated at $\text{4}.0\text{ W}$ . That’s not super bright, but it should be plenty of light for routine activities in the tent.

a. Find an expression for the induced current as a function of time if you turn the crank at frequency f. Assume that the semicircle is at its highest point at $t=0\text{ s}$ .

b. With what frequency will you have to turn the crank for the maximum current to fully light the bulb? Is this feasible