Direct "Literal" Demonstration of the Effect of a Displacement Current

Notes and Discussions

which are controlled by a single, spring-return (center-off) SP3T toggle switch mounted in a hand-held unit on a cable.

I would like to acknowledge, the substantial contributions of R. N. Euwema and J. A. Elmgren in developing this experiment.

¹ See, for instance, J. W. M. DuMond and E. R. Cohen, Rev. Mod. Phys. 25, 691 (1953).

² A. C. Melissinos, Experiments in Modern Physics (Academic, New York, 1966), pp. 2—8; The Taylor Manual, edited by T. B. Brown (Addison—Wesley, Reading, MA, 1959), pp. 392-94.

H. Kruglak, Am. J Phys. 40, 768 (1972).

⁴ The students are also given values of the individual poromet.ers for reference. The parameters dæ9 mm, mm, and p *0.9 g/cm³ were meast.n•ed by routine methods. The viscosity of bir i.s taken be 1.69 X kg/m-sec, the handbook value for '23 ⁰C decreased by the mean-free-path (mfp) correction (8%) for the 2 gin-diurn drops typical of our observations. Strictly, the mfp correction should be proportional to At^l /² • our single value of effective viscosity is in error by about 2% at the extreme fall times commonly observed (A'15, 35 sec) .

 ⁶ The posting of the original A At values in addition to the computed A V—1 M-3 /² gives the instructor a chance to spot gross arithmetic blunders, which occur all too frequently.

⁶ E. Whittaker and G. Robinson, The Calculus of Observations (Von Nostrand, Princeton, NJ, 1944), 4th ed. sec. 101, 104.

 ⁷ Similar to Experiment EF-I, A. M. Portis and H. D. Young, Berkeley Physics Labora.toriol (McGraw—Hill, New York, 1971), 2nd ed.

Direct "Literal" Demonstration of the

Effect of a Displacement Current

THOMAS R. CARVER

JAN RAJHEL

Joseph Henry Laboratories

Departnunt of Physics

Princeton University

Princeton, New Jersey 08540

(Received 26 June 1973; revised 17 July 1973)

Maxwell's displacement current density is one of the physical concepts—like magnetic induction in Faraday's Law—that requires the freshmen physics students to understand changing flux and circuital line integral paths. These concepts seem  to be anomalously diffcult to understand. Although the existence of electromagnetic radiation might seem to be an adequate test of Maxwell's theory and a demonstration of displacement currents, one often feels a more literal demonstration of displacement current is needed. This note, de- scribes a lecture-demonstration apparatus which shows the effect of the displacement current between two capacitor plates and introduces the student to the motivating idea that an induced circuital magnetic field is produced not only by a real current in a wire leading to a capacitor plate, but also—in the sense of continuity—by the displacement current between capacitor plates.

Our apparatus is simple: A toroidal coil is either

placed around a wire leading to a large pair of capacitor plates to demonstrate Ampere's law, or the toroidal coil is inserted between the capacitor plates as shown in mg. 1 to demonstrate

FIG. 1. Schematic of general setup of the demonstration showing toroidal coil in position A for Ampere's law and in position B for displacement currents: (1) capacitor plates; (2) audio oscillator; (3) matching or driving transformer described in text; (4) output transformer described in text; (5) center tap of output transformer grounded to coil shield

(not shown) and to cable shielding leading to oscilloscope; (6) differential input, fairly high gain, low frequency oscilloscope.

the effect of the displacement current. A magnetic field produced by the alternating currents of either form in the right hand terms of

B.dl=go ( 1+0ffddEt •dS)

induces, by Faraday's law,

an alternating voltage which is displayed on an oscilloscope and also on a large lecture slave, oscilliscope. The concept is completely obvious to most physicists, but the, reader who substitutes a.ct,ual numbers into the above equations for a suitably sized capacitor and coil and for convenient choices of ac frequencies will find that the induced voltage is inconveniently small. Moreover, if one must contend with a small voltage signal, then the stray capa.citive. pickup voltagc will mask the desired effect. For example, if one, uses a 10 000-turn toroidal coil of about a 30—40 cm diam, with a cross-sectional area of about 10 cm², and uses large capacitor plates with a spacing of 6—10 cm that are driven at 60 Hz by a small neon-sign transformer at several kilovolts, then the induced voltage is little more than a few microvolts and the unwanted pickup signal will be more than a few volts. Alternately, if one chooses a frequency which is high, such as 1 MHz, then special equipment such as a radio-frequency amplifier and a fast scope will be required. We believe that the demonstrati(jn set-up described in this note comes

close to optimal simplicity and, except for the construction of the coil itself, requires no special apparatus that is not commonly available in a physics laboratory or lecture-demonstration stockroom.