|LECTURE DEMONSTRATION MANUAL | Instructional Research Lab : ucla physics|
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Z.R.3 Special Relativity
Although most physicists are aware that relativity is involved in the Faraday magnet and coil induction experiment E.5.1, few exploit the full significance of it as a relativity demonstration. But this experiment demonstrates a truly relativistic effect at very low velocities. It shows, among other things, that physical results depend only on the relative motion (Einstein's first postulate of relativity, the physics is independent of the uniform motion of an inertial frame), and that electric and magnetic fields manifest themselves differently to different moving observers. In addition the experiment has the advantage of motivating relativity in the same way as Einstein was motivated, as in the quote above. This demonstration is useful as a general introduction to relativity in the non-calculus courses and as a motivation for the Lorentz transformation in a higher level special relativity course.
A good place to introduce the demonstration for the first time is just before the coverage of Faraday Induction. (Later when relativity is covered, the demonstration can be repeated and new features emphasized. Referring to the figure first hold the magnet stationary with respect to the classroom, and move the coil toward the magnet. In this situation, case A, the force that moves the electrons around the coil to produce the galvanometer readings the Lorentz force F = qv/c X B. where v is the velocity of the coil toward the magnet.
Before demonstrating the moving magnet case B, discuss with the students what they should expect to see. There is a magnetic field, but this does not affect the electrons in the coil, since their velocity is initially zero, and even after they begin to circulate around the coil, the magnetic v X B force is perpendicular to the wire and so does not cause the current. In fact, nothing the students have studied so far in E & M would lead them to expect a galvanometer reading in case B. When this proposition is put to the class, some students will object that " it shouldn't matter whether the coil or magnet is moved". If the class is pressed on this point, one can usually draw out the comment that "only the relative motion should matter". After a short discussion of Einstein's relativity principle, one can go on to perform case B. moving the magnet toward the coil. But, of course, although Einstein's postulate tells us that there must be a new force on the electrons, this new force must have a specific physical origin or description, and it is then appropriate to introduce Faraday induction or Grad X E = 1/c dB/dt. (In a non-calculus course this can be simply worded as a changing magnetic field produces a circular electric field.)
Further points that can be emphasized when the experiment is demonstrated later for relativity are:
The principles of this demonstration as presented in a non-calculus course are summarized on the next page which is available as a transparency from Art.
This demonstration was inspired by section 16.7 of Basic Physics by Kenneth W. Ford (Blaisdell Publishing Co., Waltham, Mass., 1968) The Einstein quote quote at the beginning was from the 1952 meeting honoring the centenary of Michelson's birth as quoted in Introduction to Special Relativity by Robert Resnick (John Wiley and Sons, New York, 1968).
We see Lucy and Ringo both moving, approaching each other.
The loop is stationary and the magnet is moving toward it. There is a magnetic field, but it can't produce any force on my electrons since they are stationary within the loop. Instead, the magnetic field is changing, growing stronger as the magnet gets closer, and this changing magnetic field produces an electric field which causes forces on the electrons, and drives them around the loop and produces the current in the galvanometer.
The magnet is stationary and the loop is moving toward it. The electrons in the loop, since they are moving with the loop, feel a magnetic force, F = - e/c v X B, which drives them around the loop and produces the current in the galvanometer. There is no electric field.
Electric and magnetic fields are not invariant entities themselves, but are aspects of a single entity, the electromagnetic field, which manifests itself differently to different moving observers.