For the Love of Physics (26 page)

You can visualize torque easily if you’ve ever changed a tire. You know that one of the most difficult parts of the operation is loosening the lug nuts holding the wheel onto the axle. Because these nuts are usually
very tight, and sometimes they feel frozen, you have to exert tremendous force on the tire iron that grips the nuts. The longer the handle of the tire iron, the larger the torque. If the handle is exceptionally long, you may get away with only a small effort to loosen the bolts. You exert torque in the opposite direction when you want to tighten the nuts after you’ve replaced the flat tire with your spare.

Sometimes, of course, no matter how hard you push or pull, you can’t budge the nut. In that case you either apply some WD-40 (and you should always carry WD-40 in your trunk, for this and many other reasons) and wait a bit for it to loosen, or you can try hitting the arm of the tire iron with a hammer (something else you should always travel with!).

We don’t have to go into the complexities of torque here. All you have to know is that if you run a current through a coil (you could use a battery), and you place that coil in a magnetic field, a torque will be exerted on the coil, and it will want to rotate. The higher the current and the stronger the magnetic field, the larger the torque. This is the principle behind a direct current (DC) motor, a simple version of which is quite easy to make.

What exactly is the difference between direct current and alternating current? The polarity of the plus and minus sides of a battery does not change (plus remains plus and minus remains minus). Thus if you connect a battery to a conducting wire, a current will always flow in one direction, and this is what we call direct current. At home (in the United States), however, the potential difference between the two openings of an electrical outlet alternate with a 60-hertz frequency. In the Netherlands and most of Europe the frequency is 50 hertz. If you connect a wire, say an incandescent lightbulb or a heating coil, to an outlet in your home, the current will oscillate (from one direction to the opposite direction) with a 60-hertz frequency (thus reversing 120 times per second). This is called alternating current, or AC.

Every year in my electricity and magnetism class we have a motor contest. (This contest was first done several years before me by my colleagues and friends Professors Wit Busza and Victor Weisskopf.) Each
student receives an envelope with these simple materials: two meters of insulated copper wire, two paper clips, two thumbtacks, two magnets, and a small block of wood. They have to supply a 1.5-volt AA battery. They may use any tool, they may cut the wood and drill holes, but the motor must be built only of the material that is in the envelope (tape or glue is not allowed). The assignment is to build a motor that runs as fast as possible (produces the highest number of revolutions per minute, or RPMs) from these simple ingredients. The paper clips are meant to be the supports for the rotating coil, the wire is needed to make the coil, and the magnets must be placed so as to exert a torque on the coil when current from the battery goes through it.

Let’s assume you want to enter the contest, and that as soon as you connect the battery to your coil it starts to rotate in a clockwise direction. So far so good. But perhaps much to your surprise, your coil doesn’t keep rotating. The reason is that every half rotation, the torque exerted on your coil reverses direction. Torque reversal will oppose the clockwise rotation; your coil may even start to briefly rotate in the counterclockwise direction. Clearly, that’s not what we want from a motor. We want continuous rotation in one direction only (be it clockwise or counterclockwise). This problem can be solved by reversing the direction of the current through the coil after every half rotation. In this way the torque on the coil will always be exerted in the same direction, and thus the coil will continue to rotate in that one direction.

In building their motors, my students have to cope with the inevitable problem of torque reversal, and a few students manage to build a so-called commutator, a device that reverses the current after every half rotation. But it’s complicated. Luckily there is a very clever and easy solution to the problem without reversing the current. If you can make the current (thus the torque) go to zero after every half rotation, then the coil experiences no torque at all during half of each rotation, and a torque that is always in the same direction during the other half of each rotation. The net result is that the coil keeps rotating.

I give a point for every hundred rotations per minute that a student’s
motor produces, up to a maximum of twenty points. Students love this project, and because they are MIT students, they have come up with some amazing designs over the years. You may want to take a shot at this yourself. You can find the directions by clicking on the pdf link to my notes for lecture 11 at
http://ocw.mit.edu/courses/physics/8-02-electricity-and-magnetism-spring-2002/lecture-notes/
.

Almost all students can make a motor that turns about 400 RPM fairly easily. How do they keep the coil turning in the same direction? First of all, since the wire is completely insulated, they have to scrape the insulation off one end of the wire coil so that it always makes contact with one side of the battery—of course, it does not matter which end they choose. It’s the other end of the wire that’s considerably trickier. Students only want the current to flow through the coil for half of its rotation—in other words, they want to break the circuit halfway through. So they scrape
half
of the insulation off of that other end of the wire. This means there’s bare wire for half of the circumference of the wire. During the times that the current stops (every half rotation), the coil continues to rotate even though there is no torque on it (there isn’t enough friction to stop it in half a rotation). It takes experimentation to get the scraping just right and to figure out which half of the wire should be bare—but as I said, nearly anyone can get it to 400 RPM. And that’s what I did—but I could never get much higher than 400 RPM myself.

Then some students told me what my problem was. Once the coil starts turning more than a few hundred RPM, it starts to vibrate on its supports (the paper clips), breaking the circuit frequently, and therefore interrupting the torque. So the sharper students had figured out how to take two pieces of wire to hold the ends of the coil down on the paper clips at either end while still allowing it to rotate with little friction. And that little adjustment got them, believe it or not, to 4,000 RPM!

These students are so imaginative. In almost all motors, the axis of rotation of the coil is horizontal. But one student built a motor where the axis of rotation of the coil was vertical. The best one ever got up to 5,200 RPM—powered, remember by one little 1.5-volt battery! I remember
the student who won. He was a freshman, and the young man said, as he stood with me after class in front of the classroom, “Oh, Professor Lewin, this is easy. I can build you a 4,000 RPM motor in about ten minutes.” And he proceeded to do it, right in front of my eyes.

But you don’t need to try to create one of these. There’s an even simpler motor that you can make in a few minutes, with even fewer components: an alkaline battery, a small piece of copper wire, a drywall screw (or a nail), and a small disc magnet. It’s called a homopolar motor. There’s a step-by-step description of how to make one, and a video of one in action right here (drop me a line if yours goes faster than 5,000 RPM):
www.evilmadscientist.com/article.php/HomopolarMotor
.

Just as much fun as the motor contest, in a totally different way, is another demonstration I perform in class with a 1-foot-diameter electric coil and a conducting plate. An electric current going through a coil will produce a magnetic field, as you now know. An alternating electric current (AC) in a coil will produce an alternating magnetic field. (Recall that the current created by a battery is a direct current.) Since the frequency of the electricity in my lecture hall is 60 hertz of alternating current, as it is everywhere in the United States, the current in my coil reverses every 1/120 second. If I place such a coil just above a metal plate, the changing magnetic field (I call this the external magnetic field) will penetrate the conducting plate. According to Faraday’s law, this changing magnetic field will cause currents to flow in the metal plate; we call these eddy currents. The eddy currents in turn will produce their own changing magnetic fields. Thus there will be two magnetic fields: the external magnetic field and the magnetic field produced by the eddy currents.

During about half the time in the 1/60-second cycle, the two magnetic fields are in opposite directions and the coil will be repelled by the plate; during the other half the magnetic fields will be in the same direction and the coil will be attracted by the plate. For reasons that are rather subtle, and too technical to discuss here, there is a net repelling force on the coil, which is strong enough to make the coil levitate. You can see this in the video for course 8.02, lecture 19:
http://videolectures.net/mit802s02_lewin_lec19/
.
Look about 44 minutes and 20 seconds into the lecture.

I figured we ought to be able to harness this force to levitate a person, and I decided that I would levitate a woman in my class, just like magicians do, by creating a giant coil, having her lie on top, and levitating her. So my friends Markos Hankin and Bil Sanford (of the physics demonstration group) and I worked hard to get enough current going through our coils, but we ended up blowing the circuit breakers every time. So we called up the MIT Department of Facilities and told them what we needed—a few thousand amps of current—and they laughed. “We’d have to redesign MIT to get you that much current!” they told us. It was too bad, since a number of women had already emailed me, offering to be levitated. I had to write them all back with regrets. But that didn’t stop us, as you can see by logging on to the lecture at about 471/2 minutes in. I made good on my promise; the woman just turned out to be much lighter than I’d originally planned.

Electromagnetism to the Rescue

Levitating a woman makes for a pretty good—and funny—demonstration, but magnetic levitation has a host of more amazing and much more useful applications. It is the foundation of new technologies responsible for some of the coolest, fastest, least polluting transportation mechanisms in the world.

You’ve probably heard of high-speed maglev trains. Many people find them utterly fascinating, since they seem to combine the magic of invisible magnetic forces with the sleekest of modern aerodynamic design, all moving at extremely high speeds. You may not have known that “maglev” stands for “magnetic levitation.” But you do know that when you hold magnetic poles close together, they either attract or repel each other. The wonderful insight behind maglev-trains is that if you could find a way to control that attractive or repulsive force, you ought to be able to levitate a train above tracks and then either pull or push it at
high speed. For one kind of train, which works by electromagnetic suspension (known as EMS), electromagnets on the train lift it by magnetic attraction. The trains have a C-shaped arm coming down from them; the upper part of the arm is attached to the train, while the lower arm, below the track, has magnets on its upper surface that lift the train toward the rails, which are made of ferromagnetic material.

Since you don’t want the train to latch on to the rails, and since the attractive force is inherently unstable, a complicated feedback system is needed to make sure the trains remain just the right distance away from the rails, which is less than an inch! A separate system of electromagnets that switch on and off in synchronized fashion provide the train’s propulsion, by “pulling” the train forward.

The other main type of maglev train system, known as electro-dynamic suspension (EDS), relies on magnetic repulsion, using remarkable devices called superconductors. A superconductor is a substance that, when kept very cold, has no electric resistance. As a result, a supercooled coil made out of superconducting material takes very little electrical power to generate a very strong magnetic field. Even more amazing, a superconducting magnet can act like a magnetic trap. If a magnet is pushed close to it, the interplay between gravity and the superconductor holds the magnet at a particular distance. As a result, maglevs that use superconductors are naturally much more stable than EMS systems. If you try to push the superconductor and the magnet together or pull them apart, you’ll find it quite hard to do. The two will want to stay the same distance from each other. (There’s a wonderful little video that demonstrates the relationship between a magnet and a superconductor:
http://www.youtube.com/watch?v=nWTSzBWEsms
.)

If the train, which has magnets on the bottom, gets too close to the track, which has superconductors in it, the increased force of repulsion pushes it away. If it gets too far away, gravity pulls it back and causes the train to move toward the track. As a result, the train car levitates in equilibrium. Moving the train forward, which also uses mostly repulsive force, is simpler than in EMS systems.

Both methods have pluses and minuses, but both have effectively eliminated the problem of friction on conventional train wheels—a major component of wear and tear—while producing a far smoother, quieter, and above all
faster
ride. (They still have to cope with the problems of air drag, which increases rapidly with the speed of the train. That’s why they are designed to be so aerodynamically sleek.) The Shanghai Maglev Train, which works by means of electromagnetic suspension and opened in 2004, takes about 8 minutes to travel the 19 miles from the city to the airport, at an average speed (as of 2008) of between 139 and 156 miles per hour—though it’s capable of a top speed of 268 miles per hour, faster than any other high-speed railway in the world. You can see a short video of the Shanghai train here, made by its manufacturers:
www.youtube.com/watch?v=weWmTldrOyo
. The highest speed ever recorded on a maglev train belong to a Japanese test track, where the JR-Maglev train hit 361 miles per hour. Here’s a short piece on the Japanese train:
www.youtube.com/watch?v=VuSrLvCVoVk&feature=related
.