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3. A rectangular loop of wire with mass m, width w, vertical length I, and resistance R falls out of a magnetic field under the influence of gravity, as shown in the fig. 2. The magnetic field is uniform B = Bot within the area z>0 and zero outside of that area. B=0 Figure 2: Rectangular wire loop (a) Using Lenz' law, find the direction of current flowing in the loop in fig. 2. Make sure your answer includes a statement about the change in magnetic flux. (b) Let h be the z co-ordinate of the bottom of the loop. Suppose that the loop is falling at constant velocity Ut for all h. Find an expression for the induced EMF & as a function of h. Sketch (h) for -l

3. A rectangular loop of wire with mass m, width w, vertical length I, and resistance R falls out of a magnetic field under the influence of gravity, as shown in the fig. 2. The magnetic field is uniform B = Bot within the area z>0 and zero outside of that area. B=0 Figure 2: Rectangular wire loop (a) Using Lenz' law, find the direction of current flowing in the loop in fig. 2. Make sure your answer includes a statement about the change in magnetic flux. (b) Let h be the z co-ordinate of the bottom of the loop. Suppose that the loop is falling at constant velocity Ut for all h. Find an expression for the induced EMF & as a function of h. Sketch (h) for -l

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3. A rectangular loop of wire with mass m, width w, vertical length I, and resistance R falls out of a magnetic field under the influence of gravity, as shown in the fig. 2. The magnetic field is uniform B = Bot within the area z>0 and zero outside of that area. B=0 Figure 2: Rectangular wire loop (a) Using Lenz' law, find the direction of current flowing in the loop in fig. 2. Make sure your answer includes a statement about the change in magnetic flux. (b) Let h be the z co-ordinate of the bottom of the loop. Suppose that the loop is falling at constant velocity Ut for all h. Find an expression for the induced EMF & as a function of h. Sketch (h) for -l<h<l. Clue: To use Faraday's law, you'll need to take the time derivative of the magnetic flur through the loop. (c) Find an expression for the induced current I(h). (d) Draw a free body diagram indicating the forces acting on the loop. (e) Find the terminal velocity v, in terms of the other given quantities. (f) [Bonus] Suppose that the loop is not falling at terminal velocity. At t = 0, h = 0, and the loop is released from rest. Find h(t), the velocity of the loop as it falls.
Transcribed Image Text:3. A rectangular loop of wire with mass m, width w, vertical length I, and resistance R falls out of a magnetic field under the influence of gravity, as shown in the fig. 2. The magnetic field is uniform B = Bot within the area z>0 and zero outside of that area. B=0 Figure 2: Rectangular wire loop (a) Using Lenz' law, find the direction of current flowing in the loop in fig. 2. Make sure your answer includes a statement about the change in magnetic flux. (b) Let h be the z co-ordinate of the bottom of the loop. Suppose that the loop is falling at constant velocity Ut for all h. Find an expression for the induced EMF & as a function of h. Sketch (h) for -l<h<l. Clue: To use Faraday's law, you'll need to take the time derivative of the magnetic flur through the loop. (c) Find an expression for the induced current I(h). (d) Draw a free body diagram indicating the forces acting on the loop. (e) Find the terminal velocity v, in terms of the other given quantities. (f) [Bonus] Suppose that the loop is not falling at terminal velocity. At t = 0, h = 0, and the loop is released from rest. Find h(t), the velocity of the loop as it falls.
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