Question

3. Electromagnetic Inductance. Consider a single loop under magnetic field. (a) If the area A = 0.012[m) is constant, but the magnetic field is increasing at the rate of 0.020 T/s), determine the induced emf. (Use Faraday's law; the induced emf in a loop equals the absolute value of the time rate of change of the magnetic flux through the loop.) (b) If the total resistance of the circuit is 5.0(82), find the induced current. (c) Suppose we change the apparatus so that we can change the area of the loop and keep the magnetic field constant. If B = 0.010[T] constant, but the area is increasing at the rate of 0.25[m/s], determine the induced emf and current, where the new resistance is 2.5[92]. Consider a slide-wire generator, i.e., a conducting rod L = 0.1[m] moving in a uniform magnetic field B = 0.60T). The rod, its velocity, and the magnetic field are mutually perpendicular. This rod slides on the conducting rails, forming a closed circuit. (d) In a time interval At[sec], the rod moves a distance vAt[m] and swipes a rectangular area L X vAtm?), where v = 2.5 m/s). Assuming the magnetic field is uniform, find the induced emf on the rod. (Use Faraday's law.) (e) If the total resistance of the circuit is 0.03092), find the current I[A] in the loop. (f) Consider current I[A] in a wire l[mand magnetic force on it. The magnetic force on a charge q is given by quB, where v is the velocity of the charge q in a wire. In a time interval At = 1/, we can write q = I At. Derive the force F on this wirel[m], as a function of current, length, and magnetic field strength. (g) Assume that the area is increasing. Determine the induced magnetic force on the rod. (Lenz's low tells that an induced force F[N] on the rod is the opposite direction to the velocity.) (h) To keep the rod moving at constant speed, a force stays constant in magnitude. Therefore the mechanical power P[W] = Fu. Find this P. (i) The rate at which the induced emf delivers electrical energy into the circuit i.e., power) is given by P = emf x I. This must be equal to mechanical power input studied above. Find P, and check P = P. (1) The rate of dissipation of electrical energy in the circuit resistance is P = RI? Find P, and check P = P2.