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A Different Twist on the Lorentz Force and Faraday's A Different Twist on the Lorentz Force and Faraday’s Law Bill Layton and Martin Simon n this paper we will describe some simple magnet and the conductor or is it the velocity experiments involving the magnetic force with respect to some rest frame (ether) in Ion currents and electromagnetic induc- which the magnetic fields are always at rest? tion. In every situation, the heart of the appa- We are not suggesting that the laws of ratus will be a “homopolar” or “unipolar” physics be revised, but we do want to set the magnet structure (which is nothing more than stage for a careful rethinking of some of the two cylindrical magnets with like poles held most basic and accepted laws presented in the together.) Homopolar structures make it pos- traditional high-school course. Should you sible to construct dc motors and generators desire a more detailed mathematical treatment without commutators. The experiments dis- of these ideas, see the papers by Corson4 and cussed here are not new; similar experiments Webster.5 The best brief representation of the were performed by spirit of our paper Faraday in 1831.1 was presented in a Bill Layton received his However, the expla- “Little Stinker” and B.A. from UC Riverside in nation of these ex- a “George” cartoon 1957 and his M.Ed. from Harvard in 1966. He has periments has been in an old issue of recently retired, after teach- debated by physi- The Physics Teach- 6 ing high-school physics for cists such as Fara- er. An extensive set over 30 years, mostly at day, Ampere, Hertz, of references as well Palisades High School in Weber, Lorentz, Ein- as a demonstration Los Angeles. He still stein, and others experiment of the remains heavily involved in ever since. Indeed, unipolar generator the Southern California Einstein addresses can be found on the AAPT and is working with a the homopolar gen- Fig. 1. The usual electromagnetic motor illustrated here is dif- Lecture Demonstra- ferent from the homopolar motor discussed in this article. new University-High School erator in his famous tion Home Page by physics teacher alliance 1905 paper on spe- Berg and Alley.7 group in the Los Angeles area called LAPTAG. cial relativity. Finally, an outstanding in-depth study of Currently, and for the past The problem of the homopolar motor first unipolar induction can be found in “Essay 3” 8 10 years, he directs the came to our attention during a “Show and of Arthur Miller’s book. Masters of Arts in Teaching Tell” session at a recent Southern California program in the Physics AAPT section meeting when Roger Experiments with the “Homopolar Department at UCLA. Morehouse2 presented it as a puzzle for us to Motor” Department of Physics try to explain; he even coyly suggested that First we warn you of what this experiment and Astronomy the explanation might force us to reconsider is not, even though it looks very much like the UCLA the existence of the ether! Others have specu- traditional current-carrying wire moving 405 Hilgard Ave. lated that the lack of a reaction force on the through a magnetic field. The traditional pic- Los Angeles, magnet might violate Newton’s third law and ture is something like Fig. 1, and with a little CA 90095-1547 make a perpetual motion machine possible.3 bit of hand waving and a discussion of the Our purpose here is to describe some simple charges moving in the wire, the Lorentz force [email protected] but very thought-provoking experiments that expression will predict which way the wire can be done with even the most modest equip- will move. This is not the same thing we are ment. These experiments raise interesting talking about here. questions. Do magnetic fields rotate with In our experiment the magnet itself moves rotating magnets? Is the v in the Lorentz force as a result of a current passing through a cop- equation the relative velocity between the per sleeve surrounding it, with seemingly no 474 THE PHYSICS TEACHER Vol. 36, Nov. 1998 A Different Twist on the Lorentz Force and Faraday’s Law between the centers of the two magnets. (That is, the current will flow through the copper tube only in a region where the radially directed field compo- nent is all outward or all inward.) Imagine a cross-sec- tional view of the conducting copper tube in the region Fig. 2. The homopolar magnetic structure consists of two magnets with like between the two magnets. poles facing each other inside of a conducting copper cylinder. Consider only the radially directed components of the magnetic field, assume that two north poles face one another inside of the copper tube, and further assume that the current is coming toward you, out of the page (illustrated in Fig. 3). Hand waving and the Lorentz force equa- tion should produce forces tangent to the cir- cular tube and, since the magnetic field is radially outward, the forces will be in a coun- terclockwise direction. These forces will pro- duce a torque that will rotate the tube counter- clockwise, and if it rests on the track it will move to the left. Reversing the direction of the Martin Simon received his current will reverse the direction of the torque B.A. and M.S. in 1987 from and cause the structure to move in the oppo- UC Los Angeles and is cur- site direction. Naturally, there is no paradox rently Administrator of and it is the copper tube pressing on the track Lecture Demonstrations at Fig. 3. Crossection of the homopolar armature taken per- that provides an equal and opposite force by UCLA. pendicular to its axis, through the center. the track on the copper tube, which in turn Department of Physics and moves the tube in one direction or the other. Astronomy external magnetic field to “push on”! This We still can’t pull ourselves up by our boot- UCLA paradox can be resolved, but an explanation straps; reactionless space drive must await a 405 Hilgard Ave. did not come immediately to us. The appara- breakthrough in the laws of physics! Los Angeles, tus is illustrated in Fig. 2; the key feature is However, there are a few more questions we CA 90095-1547 that the two magnets inside the copper tube can ask. What would happen if we suspended have the same poles facing one another. the magnet structure in a way such that it was [email protected] When the power supply is attached to the free only to spin and we passed a current track, the magnet structure will roll one way, through it? (In other words, if the track were and when the direction of the current is slippery, would the structure respond by spin- reversed, the magnet structure will roll in the ning only?) This is the subject of our next opposite direction. Observe that the current is investigation, but before we describe those passing through the magnet structure itself results, we think it would be appropriate to and it seems as though the structure is pulling give a few details on how we constructed the itself along by its own bootstraps! We will rolling magnet on the track apparatus so that partially resolve this “paradox” in the next readers can easily duplicate the apparatus. paragraph, so if you would like to solve it yourself, put this article down and work it out Construction Details now. For this experiment to work, the two mag- The understanding of the magnet’s motion nets should be quite powerful and the track requires an appreciation that two magnets must be perfectly level. We used two power- with the same poles facing one another pro- ful cylindrical magnets9 that just fit inside of duce a radially directed magnet field in the a 3/4-in copper pipe coupler. If you have region between the poles. It is also important access to a machine lathe, you can turn a tube to realize that the track contacts the conduct- of the correct size, but we were able to use a ing copper tube only inside of the region standard 3/4-in copper pipe coupler and two A Different Twist on the Lorentz Force and Faraday’s Law Vol. 36, Nov. 1998 THE PHYSICS TEACHER 475 slightly altered 1/2-in PVC nonmagnetic bearings on pipe caps to contain the mag- either end. Even this special nets inside of the copper cou- structure required a current pler and hold them in their of 25 A. Since mercury has repelling state. To make the been “outlawed” in schools, PVC caps fit over the copper our alternate method de- coupler, it was necessary to scribed next should prove enlarge the inside using an useful. appropriate drill bit. (Again a Remembering the Caven- lathe would help, but we are dish experiment, we were trying to keep it simple. able to build a simple torsion Carving with a pocketknife Fig. 4. Construction of the homopolar motor requires very little special pendulum to detect the very also works but takes a long equipment. small torques involved. The time.) Our track was made apparatus is illustrated in from two pieces of aluminum angle spaced the proper dis- Fig. 5 and consists of a long fine piece of monofilament tance apart and screwed to a piece of wood. If the track nylon supporting the magnet structure in a vertical posi- spacing is correct, track from a model train set can also be tion. Very fine wires are soldered to the copper tube at used.
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