In the circuit shown in Fig. P29.47, the capacitor has

Chapter 29, Problem 29.47

(choose chapter or problem)

In the circuit shown in Fig. P29.47, the capacitor has capacitance \(C = 20 \ \mu \mathrm{F}\) and is initially charged to 100 V with the polarity shown. The resistor \(R_0\) has resistance \(10 \ \Omega\). At time t = 0 the switch S is closed. The small circuit is not connected in any way to the large one. The wire of the small circuit has a resistance of \(1.0 \ \Omega/\mathrm{m}\) and contains 25 loops. The large circuit is a rectangle 2.0 m by 4.0 m, while the small one has dimensions a = 10.0 cm and b = 20.0 cm. The distance c is 5.0 cm. (The figure is not drawn to scale.) Both circuits are held stationary. Assume that only the wire nearest the small circuit produces an appreciable magnetic field through it. (a) Find the current in the large circuit \(200 \ \mu \mathrm{s}\) after S is closed. (b) Find the current in the small circuit \(200 \ \mu \mathrm{s}\) after S is closed. (Hint: See Exercise 29.7.) (c) Find the direction of the current in the small circuit. (d) Justify why we can ignore the magnetic field from all the wires of the large circuit except for the wire closest to the small circuit.