EM Induction

A: Conceptual Ideas

  1. The world’s strongest magnet can produce a steady magnetic field of 45 T. If a circular loop of wire is held in the magnetic field perpendicular to the direction of the magnetic field.
  1. What is the magnetic flux through the loop?
  2. What current would be induced in the loop?
  1. The diagram above shows four different circular loops that are perpendicular to the page. The radius of loops 3 and 4 is twice that of loops 1 and 2. The magnetic field is the same for each. Rank in order Φ1 through Φ4, from the largest to the smallest.
  1. A circular loop rotates at a constant speed about an axle in the center of the loop. The diagram above shows an edge view and defines the angle Ѳ which increases from 0⁰ to 360⁰as the loop rotates.
  1. At what angle or angles is the magnetic flux a maximum?
  2. At what angle or angles is the magnetic flux a minimum?
  3. At what angle or angles is the magnetic flux changing most rapidly?
  1. The magnetic flux through a coil of wire varies as shown in the graph above. During which time interval(s) will current be induced in the coil?
  1. A magnet dropped through a clear plastic tube accelerates as expected in free fall. A magnet dropped an aluminum tube of exactly the same length and diameter, falls more slowly. Explain the behavior of the second magnet?
  1. The figure above shows two concentric conducting loops. We will define a counterclockwise current (as viewed from above) to be positive, a clockwise current to be negative. The graph shows the current in the outer loop as a function of time. Sketch a graph that shows the induced current in the inner loop.
  1. Two loops of wire are stacked vertically one above the other. Does the upper loop have a clockwise current, counter clockwise current, or no current at the following times?
  1. Before the switch is closed.
  2. Immediately after the switch is closed.
  3. Long after the switch is closed.
  4. Immediately after the switch is reopened.
  1. A conducting loop around a region of strong magnetic field contains two light bulbs. The wires connecting the bulbs are ideal. The magnetic field is increasing rapidly.
  1. Do the bulbs glow? Why or why not?
  2. If the glow, which bulb is brighter? Explain.
  1. A metal wire is resting on a U-shaped conducting rail as shown above. The rail is fixed in position but the wire is free to move.
  1. If the magnetic field is increasing in strength, does the wire move? If yes which way does the wire move? Left, right, up, down, into the page, out of the page, clockwise, or counterclockwise?
  2. If the magnetic field is decreasing in strength, does the wire move? If yes which way does the wire move?

  1. a. from magnetic north to magnetic south
b. no current /
  1. Φ3Φ1Φ2Φ4
/
  1. a. 0o and 180o b. 90o and 270o
c. approaching and just past 90o and 270o
  1. 0 to t1
t2 to t3
t4 to t5 /
  1. The second magnet induces a current in the tube and the magnetic fields oppose each other.
/
  1. See instructor

  1. a. no current
b. clockwise current
c. no current
d. counterclockwise current /
  1. A. yes b/c current is induced in the wire. B. glow is the same b/c current is the same.
/
  1. a. yes; left b. yes; right

B. Problems

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