The generator will use a small rare earth magnet with a magnetic field strength of 1.0 T. The magnet is 0.50 inches on a side and is mounted on a shaft so that it can rotate as shown. The magnet sits in the center of a fixed square coil of wire with inner side length of L=0.51 inches. The magnetic field lines come out normal to the larger flat surfaces of the magnet. Assume that the magnet and coil are both thin enough so the geometry is simple and the fields continue straight out from the surface beyond the coil wires (do not diverge).
a) The magnet rotates at angular frequency w. Write an expression for the flux through a single loop as a function of time in terms of magnet area, coil area, and field strength. (It should include a sine function.)
b) The magnet can be rotated by a hand crank at 300 revolutions per minute. Find the amplitude of the emf that can be generated with a single turn in the coil.
c) How many turns should the coil have in order to generate an amplitude of 8 V at the rotation speed in part b?
d) The i-thingy requires 5 V and consumes 0.03 W when on. You want it to operate 1 hour on one charge. How much energy must be stored in the capacitor?
