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 B = 0.20 T field between two pole tips 10 cm apart. His idea is to build a hand-cranked generator shown in Figure. He thinks you can make enough current to fully light a R = 1.0 Ω? lightbulb rated at 4.0W. 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 has a radius of r = 5.0 cm and it is at its highest point at t = 0 s. Express your answer in terms of some or all of the variables B, R, r, f, t, and the constant ?.
B. With what frequency will you have to turn the crank for the maximum current to fully light the bulb?
