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A single rectangular loop is pulled out of a region of uniform magnetic field at a constant speed v. Suppose that the loop has a mass m and a resistance R. Its cross-sectional width is L, as shown. a. Find the induced EMF in the loop. Express your final answer in terms of B, L, and v. b. Find the induced current, including direction. Express your final answer in terms of B, L, v, and R only. Find the electric power dissipated in the loop. Express your final answer in terms of B, L, v, and R only. C.

A single rectangular loop is pulled out of a region of uniform magnetic field at a constant speed v. Suppose that the loop has a mass m and a resistance R. Its cross-sectional width is L, as shown. a. Find the induced EMF in the loop. Express your final answer in terms of B, L, and v. b. Find the induced current, including direction. Express your final answer in terms of B, L, v, and R only. Find the electric power dissipated in the loop. Express your final answer in terms of B, L, v, and R only. C.

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A single rectangular loop is pulled out of a region of uniform magnetic field at a constant speed v. Suppose that the loop has a mass m and a resistance R. Its cross-sectional width is L, as shown. Find the induced EMF in the loop. Express your final answer in terms of B, L, and v. b. Find the induced current, including direction. Express your final answer in terms of B, L, V, and R only. c. Find the electric power dissipated in the loop. Express your final answer in terms of B, L, v, and R only. a. Consider: You are pulling the loop to the right, which causes an EMF and therefore a current as you calculated in part (b) above. But meanwhile, the magnetic field exerts a force on the current you've just induced. 1. Find the magnetic force on each side of the loop – magnitude and direction! What's the net force on the loop (again, magnitude and direction). Express your answer in terms of B, L, v, and R only. 2. In order for you to pull the loop to the right, you must overcome this magnetic force. The mechanical power required is equal to Work/time or (Force)(velocity). Calculate the mechanical power you must supply in order to pull the loop against the magnetic force, in terms of B, L, v, and R only. How does the mechanical power you supply compare with the electrical power generated?
Transcribed Image Text:A single rectangular loop is pulled out of a region of uniform magnetic field at a constant speed v. Suppose that the loop has a mass m and a resistance R. Its cross-sectional width is L, as shown. Find the induced EMF in the loop. Express your final answer in terms of B, L, and v. b. Find the induced current, including direction. Express your final answer in terms of B, L, V, and R only. c. Find the electric power dissipated in the loop. Express your final answer in terms of B, L, v, and R only. a. Consider: You are pulling the loop to the right, which causes an EMF and therefore a current as you calculated in part (b) above. But meanwhile, the magnetic field exerts a force on the current you've just induced. 1. Find the magnetic force on each side of the loop – magnitude and direction! What's the net force on the loop (again, magnitude and direction). Express your answer in terms of B, L, v, and R only. 2. In order for you to pull the loop to the right, you must overcome this magnetic force. The mechanical power required is equal to Work/time or (Force)(velocity). Calculate the mechanical power you must supply in order to pull the loop against the magnetic force, in terms of B, L, v, and R only. How does the mechanical power you supply compare with the electrical power generated?
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