The following article, which includes a suggested procedure, is reproduced with the permission of the author and the American Journal of Physics.

Special relativity demonstration
  Art Huffman
  Physics Department, UCLA
  Am. J. Phys. 48(9), Sept. 1980. pp. 779-80.

"The influence of the crucial Michelson-Morley experiment upon my own efforts has been rather indirect. I learned of it through H. A. Lorentz's decisive investigations of the electrodynamics of moving bodies (1895) with which I was acquainted before developing the special theory of relativity ... What led me more or less directly to the special theory of relativity was the conviction that the electromotive force acting on a body moving in a magnetic field was nothing else but an electric field."
        --Albert Einstein [1]

Although many physics instructors are aware that relativity is involved in the Faraday magnet and coil induction experiment, few exploit the full significance of it as a relativity demonstration. This note is to remind teachers that this experiment demonstrates a truly relativistic effect at very low velocities. The experiment shows, among other things, that physical results depend only on the relative motion (Einstein's first postulate of special relativity, the physics is independent of the uniform motion of the inertial frame), and that electric and magnetic fields manifest themselves differently to different moving observers.[2] In addition the experiment has the advantage of motivating special relativity in the same way as Einstein himself was motivated, as in the quote above. This demonstration is useful as a general introduction to relativity in the noncalculus 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 in a general course is just before the coverage of Faraday induction. (Later, when relativity is covered, the demonstration can be repeated and new features emphasized.) Refering to Fig. 1, 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 reading is the Lorentz magnetic force F = qv/c x B, where v is the velocity of the coil toward the magnet (see Fig. 2).

Before demonstrating the moving magnet, case B, discuss with the students what they should expect  to see. There is a magnetic field, but it does not affect the electrons in the coil since their velocity is initially zero. 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 deflection in case B. When this proposition is put to the class, some students will object that "it shouldn't matter whether the coil or the 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. But, of course, there still must be a specific physical origin for the force on the electrons, and it is then appropriate to introduce the Faraday induction or Del x E = (1/c)dB/dt law. (In a noncalculus 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 as follows:

One, it is the relative  motion that produces the same physical result in both cases A and B, a certain deviation of the galvanometer needle.

Two, in Case A there is only a magnetic field in the classroom, but in case B there is also an electric field in the classroom. It is this electric field that is moving the electrons to cause the galvanometer deflection in case B. In the older texts the force due to the electric field was called the electromotive force as in Einstein's quote above.

Three, the demonstration shows the Lorentz transformation of the electromagnetic field in that in a frame of reference moving through a stationary B  field, there is also an E  field.

Four, the galvanometer deflection is truly a relativistic effect, proportional to v/c.  This is most easily seen in the cgs system where the current i = (lB/R)(v/c),  with l  the length of the wire in the coil and R  its resistance. It is interesting to ask the advanced students why a relativistic effect can easily be seen here even though v/c ~ 10^-8. The reason is the same reason why a current carrying wire produces a measureable magnetic field (also a relativistic effect). The magnetic field of a single electron moving with velocity v is

            e    v
     B = - ---- --- x r .
            r3   c
        

Here the velocity is the drift velocity of the electrons v = v_d ~ 10^-2 cm/sec, so v/c ~ 10^-12, but the wire has lots  of electrons.

The principles of the demonstration as presented in the noncalculus course are summarized in Fig. 3.

[1] Albert Einstein at a 1952 meeting honoring the centenary of Michelson's birth as quoted by Robert Resnick, Introduction to Special Relativity,  (Wiley, New York, 1968).
[2] This demonstration was inspired by Kenneth W. Ford, Basic Physics  (Blaisdell, Waltham, MA, 1968), Sec. 16.7.