Question

# . A rectangular coil with 50 turns is placed in a magnetic as shown in Fig. 1. The coil lies in the xzplane and is free to rotate about the

x axis through its middle. A magnetic field with B = 0.60 Tis pointing in the y direction. The coil carries a current of 0.50 A in the direction shown in the diagram. The lengths of the long and short sides are 5.0 cm and 2.5 cm, respectively, and the total mass of the coil is 0.53 kg. (a) Calculate the frequency of the oscillations that occur when the coil is rotated by a small angle O about the x-axis away from the orientation shown in Fig. 1 and allowed to turn freely. (You may assume that the mass in the coil is distributed evenly along the wires.) (b) Calculate the amount of work done to turn the coil through 180° starting from its equilibrium position by integrating rd0 from 0 = 0 to r, where r is the torque, and 0 is the angle between the dipole and the field. (c) What is the magnetic energy of the coil when theta = 0 and when theta = pi? How does this answer relate to the previous question? (d) Describe what would happen if the direction of the current were rapidly reversed while the coil is oriented as shown in Fig. 1.

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