Problem Set 9

# Problem Set 9 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Fall 2007 Turn in at your table during class labeled with your name and group (e.g. L02 7A) Problem Set 9 Due: Wednesday, November 7 th at class beginning (before 10:15/12:15) This problem set focuses on material from classes 21-23 (week 9). Textbook references can be found at the top of the summaries from these days. WARNING : Start early, this is a very long problem set. Warm Up Problem 1: Magnet Moving Through a Coil of Wire Suppose a bar magnet is pulled through a stationary conducting loop of wire at constant speed, as shown in the figure below. Assume that the south pole of the magnet enters the loop of wire first, and that the center of the magnet is at the center of the loop at time t = 0. (a) Sketch qualitatively the magnetic flux B Φ through the loop as a function of time. (b) Sketch qualitatively the current I in the loop as a function of time. Take the direction of positive current to be clockwise in the loop as viewed from the left. (c) What is the direction of the force on the permanent magnet due to the current in the coil of wire just before the magnet enters the loop? (d) What is the direction of the force on the magnet just after it has exited the loop? (e) Do your answers in (c) and (d) agree with Lenz's law? (f) Where does the energy come from that is dissipated in ohmic heating in the wire? Problem Set 09 p. 1 of 1

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Sample Exam Problem… Problem 2: Faraday’s Law A conducting rod with zero resistance and length w slides without friction on two parallel perfectly conducting wires. Resistors R 1 and R 2 are connected across the ends of the wires to form a circuit, as shown . A constant magnetic field B is directed out of the page. In computing magnetic flux through any surface, take the surface normal to be out of the page, parallel to B . (a) The magnetic flux in the right loop of the circuit shown is (circle one) 1) decreasing 2) increasing. What is the magnitude of the rate of change of the magnetic flux through the right loop? (b) What is the current flowing through the resistor R 2 in the right hand loop of the circuit shown? Gives its magnitude and indicate its direction on the figure. (c) The magnetic flux in the left loop of the circuit shown is (circle one) 1) decreasing 2) increasing. What is the magnitude of the rate of change of the magnetic flux through the right loop? (d) What is the current flowing through the resistor R 1 in the left hand loop of the circuit shown? Gives its magnitude and indicate its direction on the figure. (e) What is the magnitude and direction of the magnetic force exerted on this rod? Analytic Problems… Problem 3: Coupled Rods Two rods slide without friction on two conducting rails separated by a distance w , in the presence of a constant background magnetic field B , as shown in the diagram. The mass of each rod is m and each rod has a resistance R . The rails have no resistance. At time t , the rod on the left is a distance 1 () x t from the origin, and the rod on the right is a distance 2 x t from the origin.
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Problem Set 9 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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