5K10.80 Homopolar Generator

PURPOSE: To demonstrate generation of DC voltage with the rotational motion of a magnet and a conductor using a method which may involve an explanation other than electromagnetic induction. This demonstration is also known as the "Motional EMF Demonstration", the "Homopolar Generator" and the "Unipolar Motor".

DESCRIPTION: When the conductor plate is made to rotate while the magnet is stationary a voltage is generated. And when the magnet and the conductor are both rotated together the voltage is generated. But if the magnet is made to rotate while the conductor is stationary the voltage is not generated.

A rotator is used to spin up a strong (over 10 kilogauss) cylindrical magnet to 1728 RPM. Brushes positioned on the axis of rotation and the "equator" of the bar magnet (midway between the two poles) are attached to a digital voltmeter or a Pasco electrometer. A small dc voltage of about 15 milli-volts is measured. Reversing the direction of rotation or reversing the ends of the magnet causes the voltage to reverse in sign.

The explanation of this device is perhaps problematic. Many people believe that because there is no change in flux in the wire loop this cannot be an electromagnetic induction effect; the only explanation lies in special relativity. Other theoreticians disagree.

SUGGESTIONS: This gizmo is sometimes called a "homopolar" generator. This is a nice experiment to start arguments in a graduate course on electromagnetic theory.

References:

K2-64: UNIPOLAR GENERATOR

R. J. Stephenson, Experiments with a Unipolar Generator and Motor, AJP 5, 108-110 (1937).

Dale R. Corson, Electromagnetic Induction in Moving Systems, AJP 24, 126-130, ( 1956).

David L. Webster, Relativity in Moving Circuits and Magnets, AJP 29, 262-268 (1961).

Thomas D. Strickler, Variation of the Homopolar Motor, AJP 29, 635 (1961).

A. K. Das Gupta, Unipolar Machines, Association of the Magnetic Field with the Field-Producing Magnet, AJP 31, 428-430 (1963).

David L. Webster, Schiff's Charges and Currents in Rotating Matter, AJP 31, 590-597 (1963).

Thomas Strickler, Motional emf's and the Homopolar Motor, AJP 32, 69, (1964).

Little Stinkers: Electromagnetic Induction, TPT 4, 1966.

R. Becker, "Electromagnetic Fields and Interactions, Blaisdell Pub. Co., 378-383, (1964).

P. Lorrain and D. Corson, Electromagnetic Fields and Waves, W. H. Freeman, 338-343, 657-664, (1970).

Robert D. Eagleton and Martin N. Kaplan, The radial magnetic field homopolar motor, AJP 56, 858-859 (1988).

Daniel F. Dempsey, The rotational analog for Faraday's magnetic induction law: Experiments, AJP 59, 1008-1011 (1991).

J. Guala Valverde and P. Mazzoni, The principle of relativity as applied to motional electromagnetic induction, AJP 63, 228-229 (1995).

Gerald N. Pellegrini and Arthur R. Swift, Maxwell's equations in a rotating medium: Is there a problem?, AJP 63, 694-705 (1995).

Richard E. Berg and Carroll O. Alley, Unipolar Generator: A Demonstration of Special Relativity - Department of Physics and Astronomy, Univ. of MD- College Park.

Aurthur I. Miller, Frontiers of physics, 1900-1911 Selected Essays: Unipolar Induction: A Case Study of the Interaction Between Science and Technology, 153-180, Birkhauser at Boston, MA.

Panofsky and Phillips, Classical Electricity an Magnetism, pages 240, 342-345.

J. B. Hertzberg, S. R. Bickman, M. T. Hummon, D. Krause, Jr., S. K. Peck, and L. R. Hunter, Measurement of the relativistic potential difference across a rotating magnetic dielectric cylinder, AJP 69, 648-654 (2001).

Bill Layton and Martin Simon, A different twist on the Lorentz force and Faradays law, TPT 36, 474-479 (1998).

Stanislaw Bednarek, Unipolar motore and their application to the demonstration of magnetic field properties, AJP 70, 455-458 (2002).

Jorge Guala-Valverde, Pedro Mazzoni, and Ricardo Achilles, The homopolar motor: A true relativistic engine, AJP 70, 1052-1055 (2002).

Wojciech Dindorf, Unconventional dynamo, TPT 40, 220-221 (2002).

Alexander L. Kholmetskii, One century later: Remarks on the Barnett experiment, AJP 71, 558-561 (2003).

Directions on making an apparatus for demonstrating motional EMF. Reference: Am. Phys. Teacher, 3,57,1935.

EALING MOTIONAL EMF DEMONSTRATION

Apparatus consists of an aluminum disc and circular magnet mounted on a common horizontal axis. Both are free to rotate independently about that axis. A pair of sliding contacts make electrical connection to the aluminum disc and are connected to a pair of binding posts on the supports.
A ballistic galvanometer can be connected to the apparatus with banana plugs. No other electrical connections are required.

The following demonstrations can be performed with the disk:

Rotating disc; stationary magnet
As indicated in the previous section, when the disc is rotated clockwise, the field is so directed as to cause a separation of the charges with the negative near the center and positive near the rim. If a circuit is completed by connecting a point in each of these two regions to a galvanometer, the latter will indicate a current. The direction will be determined by Lenz's Law and the magnitude will depend upon the induced emf (calculated in the previous section) and the resistance of the circuit.
Stationary conducting disc; rotating magnet
When the conducting disc is kept at rest and the magnet is rotated, no current is observed when the galvanometer is connected as before.
The magnetic field of the ceramic disc is uniform and symmetric with respect to the axis of rotation. Therefore, although the source of B (the ceramic disc) is rotating, the field itself, B, is not changing with time at any point in space. We cannot speak of moving B. B is a field quantity which may or may not change with time at a point in space, or it may or may not be spatially uniform at a particular time. The v in the expression v x B refers to the velocity of the conductor with respect to the observer. Since the conductor in this case is stationary, v is zero and there is no motional emf.
Rotating disc; rotating magnet
As stated above, the motion of the magnetic disc is immaterial. Therefore, as long as the conducting disc is rotating, the galvanometer will indicate a current as in the first case.
Rotating disc with galvanometer leads connected directly to the disc
If the galvanometer branch of the circuit could be arranged to move with the conducting disk, no emf would be developed. In this case, with a uniform B, one could show that there would be no change in flux through the circuit consisting of a radius of the disc and the galvanometer branch. Or, if one wishes to consider that there is a contribution to an emf from the radius of the moving disc, one can show that there would be an opposing contribution from the section of the galvanometer branch that runs parallel to this radius.
To simulate this situation, two holes are provided on a radius of the disc for banana jacks and leads. If these leads are then twisted and connected to a galvanometer so that the area exposed to the field is constant as the disc rotates with the leads, no change in flux threads the circuit and the galvanometer reads zero. This arrangement permits rotation through only 300º, but it is sufficient to demonstrate this case.
If the galvanometer branch could be moved while the disc is kept stationary, a motional emf would be developed whether or not the disc rotates. The analysis would be the same as in the first two cases.

Feynman, in his "Lectures on Physics", devotes section 17-2 to "Exceptions to the 'Flux Rule'". By flux rule, he means Faraday’s Law,

E = - df_m/dt.
There are two ways one might have an exception to this rule: df_m/dt = 0 and E ¹ 0 or df_m/dt ¹ 0 and E = 0. He says that if there is any doubt whether the flux rule works one should appeal to the two "fundamental equations":

F = q (E + v x B)
and

Ñ x E = - ¶B/¶t.
The Faraday Disc (Ealing Motional EMF Demonstration) is an example of the case in which df_m/dt = 0 but E ¹ 0. In this case, if no current is allowed to flow in an external circuit, then

E = - v x B,
F being zero (after an extremely short time required to reach equilibrium) in the Lorentz force law equation. Then,

E = ò E dl = - ò (v x B) dl
where the line integral is taken between the two points of contact to the disc.
Feynman draws a schematic of an apparatus for which df_m/dt ¹ 0 but E = 0. We have modified this idea into a constructable apparatus. You may have to spend some time convincing yourself that this apparatus is similar to Feynman's.
To demonstrate this apparatus, you must first convince yourself and class that it is sensitive enough to give a deflection if an emf is present. To do this, simply hold the copper rod across the gap at the end of the circuit board away from the terminals. This will provide you with a circuit of one turn. Slowly pass the card into the magnetic field of a rather large magnet. Observe that there is a good deflection.
Having convinced yourself of the sufficient sensitivity of the apparatus, adjust the magnet and card so that the copper rod rolls across the card contacting in turn each pair of the circuit elements. When the rod reaches the terminal end of the circuit board, there is no longer any flux in the circuit. So, df_m/dt ¹ 0 but E = 0. This is easy to understand according to the two "fundamental equations". ¶B/¶t = 0, so there is no emf from this equation. Further, if no current is allowed to flow in the circuit, F = 0, so

E = - v x B,
or

E = ò E dl = - ò (v x B) dl
where this integral extends only over a length about equal to the gap width, which, in principle, can be made as small as you like. So, according to the Lorentz law, E is approximately 0.
Some will argue about this analysis, saying that there is a way to make Faraday’s law yield the correct results. This is probably so, but the point is to see how easy the explanation is with the two "fundamental equations".

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Updated by JZ on 1/25/2007