A rectangular metal loop with sides of length d and g has total electrical resistance R. It is attached to a wooden (i.e. insulating) rod of length a as shown in the figure below. The stick and rod are rotating around the y-axis in uniform circular motion at constant angular frequency w. The period of this rotational motion is T. The drawing isn't perfect, but the rod rotates in the x-z plane, and the loop is oriented such that when the the angle 0 that the rod makes with the x-axis is zero, the loop lies flat in the x-y plane. There is a constant magnetic field everywhere in space B = BZ. At time t = 0, the angle 0 = 0, so that 0 = wt. For numeric questions, you may take a = 1 m, d = 0.2 m, g = 0.3 m, R = 0.02 0, w = 10T radians/sec, and B = 0.05 Tesla. For all other parts, write symbolic answers. B = BZ B = BZ Z Z a 0(t) = wt 8 (t) = wt X X Perspective view Side-on view down y-axis (a) Numeric: What is the period of the rotational motion T? ANSWER: T = 0.2 s. (b) What is the magnetic flux & through the loop as a function of time t?(c) What is the induced emf as a function of time t? (d) What is the current in the loop I(t)? (e) Numeric: What is the current (magnitude and direction) at (i) 0 = 45(7/4) and (ii) 0 = 120 (27/3)? ANSWER: (i) I = 3.33 A, circulating counter clockwise when viewed from above, and (ii) I = 4.08 A, circulating clockwise when viewed from above. (f) What is the instantaneous power dissipated in the loop as heat via resistive heating P(t)? (g) What is the total energy dissipated as heat in the ring over one full revolution of the loop and rod about the y-axis? (Hint: this requires an integral.) (h) Numeric: Compute the numeric value of the total energy dissipated as heat over one revolution. ANSWER: 0.044 J