Direct "Literal" Demonstration of the Effect of a Displacement Current, страница 3

The demonstration proceeds as follows: The toroidal coil is brought near the wire leading to the upper plate of the capacitor. If shielding is done well there is virtually no signal visible, to the. students on the oscilloscope. Then the, upper lead wi re is unplugged from the banana plug connector and reattached so that the toroidal coil encircles it, as shown .in position A, Fig. 1. There immediately appears a several millivolt signal at 20 kHz on the oscilloscope, and as one would expect from Ampere's law, this signal remains completely constant no matter where the coil is held, as long as the wire to the capacitor plate remains inside. To demonstrate that a displacement current also gives an effect, one unplugs the wire t.o the upper plate, removes the coil, reconnects the wire to the capacitor plate, and slowly inserts the, toroidal coil into the capacitor between the plates as shown as position B in Fig. 1. The signal now grows continuously until

248 / March 1974

it reaches the maximum value determined by that fraction of lines E or D enclosed within the toroidal coil. In our case this was a signal about of the size of the original Ampere's law signal with the. wire inside. It is worth pointing out that although this demonstration could be carried out with a portion of a torus or a section of straight coil, such a complete torus makes the demonstration of Ampere's law especially convincing because of the fact that the induced signal seen on the oscilloscope. is completely position independent and depends only on whether the wire is inside or outsido, the loop.

There is a pedagogical flaw or "swindle" in most atternpts to demonstrate the effects of ^areal" fields and this demonstration is no exception. When one inserts a probe into the capacitor as we do here, some of the lines of displacement current, go to the coil shield and cause real currents to flow, so that it is not unambiguously clear that the effect cornes from displacement currents. How- ever, either the lecturer rnay make quantitative estimates of the effect to show that it does coine primarily from real lines of displacement current through the toroidal core, or else the demonstration will be of value in providing the student with a clear display of the logic and the geometry, though only in a qualitative sense.

If one wishes to pursue tho question of displacement currents in this geometry to a greater degree of sophistication, we must remind the reader that the magnetic field which we deinonstrate in this "quasi-static" regime (certainly valid at 20 kHz) can be described entirely by the Biot—Savart law if one takes into account all of the real currents that flow, including the radial currents in the capacitor plates, However, the, Biofr Sava.rt law itself is derivable from the, coinplet,o forms of Maxwell's equations. This point is discussed in a few textbooks, ^l and the lecturer must deal with this difficult problem as he chooses,

Variations will certainly suggest themselves. Some may wish to have. the. radius of the capacit,or plates suffciently small in order that the toroid may be moved continuously so as to encircle, first the wire and then the capacitor while showing no change in induced signal. Wc felt it to be more dramatic not to do so. The use of permeable magnetic material in the toroid would certainly increase thc size. of the induced signal. We did not want to do so because of pedagogical simplicity, and also because of weight. Furthermore, we estimated that magnetic nonlinearities and eddy current effects would destroy the dramatic fact of a null signal when the capacitor wire, did not pass