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.An aluminum ring of radius r] = 5.00 cm and resistance 3.00 X 10'4 is placed around one end of a long air- core solenoid with 1 000 turns per meter and radius r2 = 3.00 cm as shown in Figure P31.11. Assume the axial component of the eld produced by the solenoid is one- half as strong over the area of the end of the solenoid as at the center of the solenoid. Also assume the sole- noid produces negligible eld outside its cross-sectional area. The current in the solenoid is increasing at a rate of 270 A/s. (a) What is the induced current in the ring? At the center of the ring, what are (b) the magnitude and (c) the direction of the magnetic eld produced by the induced current in the ring? Figure P31.11 Problems 1] and 12. xxxxxx xxxxxx gal Figure P3125 Problems 26 through 29. 27. Figure P3126 shows a top view of a bar that can slide \"Ion two frictionless rails. The resistor is R = 6.00 9., and a 2.50-T magnetic field is directed perpendicularly downward, into the paper. Let f = 1.20 m. (a) Calcu- late the applied force required to move the bar to the right at a constant speed of 2.00 m/s. (b) At what rate is energy delivered to the resistor? 79. Two infinitely long solenoids (seen in cross section) pass through a circuit as shown in Figure P31.79. The magnitude of B inside each is the same and is increase ing at the rate of 100 T/s. What is the current in each resistor? 0.500 m 0.500 m 7 = 0.100 m To = 0.150 m X XxX 6.00 0 XxX 3.00 0 5.00 0 0.500 m in Bout Figure P31.7942. A 100-turn square coil of side 20.0 cm rotates about a verti- cal axis at 1.50 X 103 rev/min as indicated in Figure P31.42. 20.0 cm The horizontal component of the Earth's magnetic field at the coil's location is equal to 2.00 X 10 5 T. (a) Calculate the maxi- 20.0 cm mum emf induced in the coil by this field. (b) What is the orien- tation of the coil with respect Figure P31.42 to the magnetic field when the maximum emf occurs