Physics 9 WS M5 (rev. 1.0) Page 1

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Rosalind Stokes
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1 Physics 9 WS M5 (rev. 1.0) Page 1 M-3. Faraday s Law Questions for discussion 1. In the figure below, there is a non-uniform magnetic field pointing into the page. a) If you move the metal loop to the right, will a current be induced in it? b) If so, will the induced current be clockwise or counter-clockwise? c) Suppose you want to move the loop to the left at constant speed. Will you have to exert any force to do this? Why or why not? d) Suppose instead that you want to move the loop upwards. Will a current be induced in it? Why or why not?

2 Physics 9 WS M5 (rev. 1.0) Page 2 2. The diagram below shows an infinitely long current-carrying wire, with two metal loops nearby. By means of a current generator (not shown), we cause the current in the wire to increase with time. a) Will a current be induced in loop 1? If so, will it be clockwise or counter-clockwise? b) Will a current be induced in loop 2? If so, will it be clockwise or counter-clockwise? 3. A crude current generator consists of a loop of wire with area A and resistance R. The loop is connected to a handle, so that someone can cause it to rotate within a uniform magnetic field B 0 that points upwards. a) How does this device generate current? b) Why will you have to do work in order to turn the handle?

3 Physics 9 WS M5 (rev. 1.0) Page 3 Problems 1. A rectangular loop of wire has length L, height H, and resistance R. The loop balances on one edge and slides frictionlessly with speed v 0. It encounters a region of uniform magnetic field B 0 pointing into the page. There are five time intervals of importance here: i. The time before the loop enters the ii. The time while the loop is partly within the iii. The time while the loop is entirely within the iv. The time while the loop is partly out of the v. The time while the loop is entirely outside the field. a) For each of the five time intervals, determine the sense of the induced current (clockwise, counter-clockwise, or no current). b) Taking clockwise currents to be positive, sketch a graph of the induced current versus time. c) Do you think that the final speed of the loop will be less than v 0, equal to v 0, or greater than v 0? Why? d) Ignoring the effect alluded to in part (c), determine the magnitude of the induced current for each of the five time intervals. 2. The rectangular metal loop has height H, width L, and resistance R. Initially the loop is situated halfway within a uniform magnetic field B 0. You want to pull the loop out of the field at a constant speed v 0. a) Explain why you are, in fact, going to have to do work in order to extract the loop. (Try to give more than one explanation.) First method: Forces b) During the time you are pulling the loop out of the field with speed v 0, what is the magnitude of the induced current in the loop? Is this clockwise or counter-clockwise? c) What force does the magnetic field exert on each segment of the loop during this time? d) What is the net magnetic force on the loop? In which direction does it point? In this problem, we will calculate in two different ways the amount of work you will have to do in order to extract the loop. (continued, next page)

4 Physics 9 WS M5 (rev. 1.0) Page 4 e) In order to pull the loop to the left with constant speed v 0, what force will you have to exert? f) Over what distance will you have to exert this force? g) How much work will you have to do in order to extract the loop? Second method: Energy h) During the time you are pulling the loop out of the field with speed v 0, what is the rate at 3. The metal loops shown below are concentric circles lying in the same plane. which heat is being dissipated by the loop s resistance? i) For how long a time will heat energy be dissipated at this rate? j) How much total heat energy will be dissipated during the time you pull out the loop? k) How much work will you have to do in order to extract the loop? l) Do your answers for part (g) and part (k) agree? b) How strong is this magnetic field at the center point? c) Assume that the small loop is so small that the magnetic field of the large loop is approximately uniform over its extent. Under this assumption, what is the flux of the magnetic field through the small loop? Now imagine that, starting at t=0, the current generator causes the current in the large loop to increase at a steady rate, until it reaches 4i 0 at time t=t. After time t=t, the current in the large loop remains steady at 4i 0. d) Sketch the current in the large loop as a function of time. The large loop of radius 20a is connected to a current generator. The small loop of radius a is not connected to anything. a) Suppose that a current i 0 is flowing clockwise around the large loop. Sketch the magnetic field created by the large loop. e) During the time 0 < t < T when the current in the large loop is increasing, will a current be induced in the small loop? Why or why not? If so, then will the induced current be clockwise or counter-clockwise? f) If the resistance of the small loop is R, then find the magnitude of the current induced in the small loop.

5 Physics 9 WS M5 (rev. 1.0) Page 5 4. A rectangular metal loop has height H, length L, and resistance R. It sits a distance D from a long straight wire. The current in the long straight wire varies in time according to i(t) = i o (1 t T ) for t < T i(t) = 0 for t > T. a) What is the magnetic flux, Φ B, through the loop as a function of time? [Careful: the magnetic field is not uniform over the loop. What must you do to find the flux?] b) What is the emf induced around the loop as a function of time? c) What is the current induced in the loop? Which way does this current flow?

Agenda for Today. Elements of Physics II. Forces on currents

Agenda for Today. Elements of Physics II. Forces on currents Forces on currents Physics 132: Lecture e 14 Elements of Physics II Agenda for Today Currents are moving charges Torque on current loop Torque on rotated loop Currents create B-fields Adding magnetic fields