W9_parallel_resonance.eps

Week 8: Faraday’s Law and Induction 271

Example 8.4.2: Rectangular Loop Pulled from Field

R

r

B (in)

F

Figure 98: A rectangular loop of wire is pulled out of a region of uniformmagnetic field as shown.

In figure 98 you can see a wire loop (rectangular, although this makes no real difference) being
pulled from the field. A typical short answer question might show thispicture, or a similar picture,
of a loop of any shape you like being pushed into or pulled out of a magnetic field and ask you the
following questions:

• What is thedirectionof the inducedE~-field/current in the wire as it is being pulled out (or
  pushed in)?


• What is the direction of themagnetic forceacting on the loop while this is going on (in either
  direction)?


• A trick question might show you the loopcompletely insidethe uniform field (so it isn’t actually
  coming out!) and ask the same questions.

What are the answers?

• When the loop is being pulled out, the flux through the loop isdecreasing. The sad little
  loop doesn’t want the flux to go away, so it generates a clockwise current whose magnetic field
  sustains the disappearing flux.


• The force on this current (check)resists the motion of the loop out of the field.


• If the loop were entirely in the field, the flux wouldn’t be changing as it moved and there would
  be no current and no net force.

This example isalmostidentical to a rod on rails problem, is it not? For a specified geometry
and massmof wire loop and speedv, you might well be able tocomputethe current, the force, the
acceleration, the trajectory.

8.5: More Rod on Rails Problems

Example 8.5.1: Rod on Rails with Battery

In figure 99 above, the switch is closed at timet= 0 with the rod (of massMand lengthL) sitting
at rest on a pair of frictionless conducting rails that are on the other end connected by a resistorR