Problem Set 9 Solutions

Problem Set 9 Solutions - MASSACHUSETTS INSTITUTE OF...

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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. L01 6B) Problem Set 9 Solutions 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 positive direction for flux is to the right. Assume that the north 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. Here the field points to the left through the loop at all times, so the flux is negative and the plot of flux vs. time looks like: t (b) Sketch qualitatively a graph of 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. The current will first oppose a leftward flux by going clockwise. It will then oppose the loss of leftward flux by going counterclockwise t Problem Set 09 Solutions p. 1 of 1
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(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? As the magnet approaches the loop, the force on the magnet must be resistive so the force on the magnet points to the left. Note that the induced current flows clockwise (as seen from the left hence ) as the magnetic approaches the loop, so the current acts as a 0 ind I < magnetic dipole with the dipole moment pointing to the right. We can model the current loop as a magnet, with the north pole facing to the right, hence the permanent magnet and the dipole have south poles facing each other indicating that the magnetic force is repulsive. (d) What is the direction of the force on the magnet just after it has exited the loop? The force is still resistive so it points to the left on the permanent magnet. The induced current has changed direction and now flows counterclockwise (as seen from the left hence ). Thus dipole moment of the loop points to the left. Again, we model the 0 ind I > current loop as a magnet, with the north pole facing to the left, hence the permanent magnet and the dipole have opposite poles facing each other indicating that the magnetic force is now attractive. (e) Do your answers in (c) and (d) agree with Lenz's law? Yes. See solutions to part (c) and (d). (f) Where does the energy come from that is dissipated in ohmic heating in the wire? The magnet is pulled a constant speed so the energy is coming from the source that is pulling the magnet. Problem 2: Faraday’s Law A conducting rod with zero resistance and length w slides without friction on two parallel perfectly conducting wires.
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This homework help was uploaded on 04/07/2008 for the course 8 8.02 taught by Professor Hudson during the Fall '07 term at MIT.

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Problem Set 9 Solutions - MASSACHUSETTS INSTITUTE OF...

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