A farmer decides to \"borrow\" some electricity from a nearby power line to run his milking machine. After spending some time on the intemet reading about Faraday's law, he realizes that by weapping some wire around his barn he can inductively pick up power from the line without making any physical connection to the power line. The power line is a single wire carrying an alternating current of 1000A at 60Hz [I(t)=1000A cos(2 pi SOHz t)]. The wire is located 15 meters from the center of the barn, which is a square with sides of length 20m. We want to estimate how much wire the farmer will need to do his job. (a) (3) What is the strongest magnetic field produced by the power line at the closest side, the furthest side and the middle of the barn at the same height (and plane) as the power line? (b) (1.5) Estimate the maximum ux of magnetic field through one turn of wire around the barn. You can use the value of the field at the center of the barn as the average field over the barn. (c) (1.5) Use Faraday's law to calculate the maximum EMF generated by the changing ux on a single loop of wire. (d) (2)What is the average power delivered by a single turn of wire assuming that the milking machine has a resistance of 40 Ohms? You may ignore the resistance and self-inductance of the wire loop. (e) (1) Assuming the milking machine needs 1kW of average power, how many turns of wire around the barn will be required? You may still ignore the resistance and self-inductance of the wire loop. (f) (1) In three sentences or less, describe how the power company could determine that the farmer had hooked up the milking-machine powering system, using information on voltages and currents measured at the power station far from the farmer. \ Y