For the Love of Physics (27 page)

There are lots of hilarious and informative YouTube videos featuring maglev technology. This one, in which a boy levitates a spinning pencil with six magnets and a little modeling clay, features a demonstration you can reproduce easily at home:
www.youtube.com/watch?v=rrRG38WpkTQ&feature=related
. But also have a look at this one, using a superconductor design. It shows a model train car zipping around a track—and even has a little animated explanatory section:
www.youtube.com/watch?v=GHtAwQXVsuk&feature=related
.

My favorite Maglev demonstration, however, is the wonderful little spinning top known as the Levitron. You can see different versions at
www.levitron.com
. I have an early one in my office that has delighted hundreds of visitors.

Maglev train systems have genuine environmental advantages—they use electricity relatively efficiently and don’t emit greenhouse gases in exhaust. But maglev trains don’t produce something for nothing. Because most maglev tracks are not compatible with existing rail
lines, maglev systems require a lot of up-front capital, which has worked against them being in widespread commercial use so far. Even so, developing more efficient and cleaner mass transit systems than what we use today is absolutely essential for our future if we’re not going to cook our own planet.

Maxwell’s Extraordinary Achievement

Many physicists think that James Clerk Maxwell was one of the most important physicists of all time, perhaps right behind Newton and Einstein. He contributed to an incredible range of fields in physics, from an analysis of Saturn’s rings, to exploring the behavior of gases, thermodynamics, and the theory of color. But his most dazzling achievement was developing the four equations describing and linking electricity and magnetism that have become known as Maxwell’s equations. These four equations only appear simple; the math behind them is pretty complicated. But if you’re comfortable with integrals and differential equations, please take a look at my lectures or surf around on the web to learn about them. For our purposes, here’s what Maxwell did in simpler terms.

Above all, Maxwell unified the theory of electricity and magnetism by showing these two phenomena to be just one phenomenon—electromagnetism—with different manifestations. With one very important exception, the four equations are not his “laws” or inventions; they already existed in one form or another. What Maxwell did, however, was bring them together in what we call a complete field theory.

The first of these equations is Gauss’s law for electricity, which explains the relationship between electric charges and the strength and distribution of the electric fields they create. The second equation, Gauss’s law for magnetism, is the simplest of the four and says several things at once. It says that there are no such things as magnetic monopoles. Magnets always have a north and south pole (we call them dipoles) as opposed to electricity which allows for electric monopoles (a monopole is either a positively charged particle or a negatively charged one). If you break one
of your magnets (I have many on my refrigerator) in two pieces, each piece has a north and a south pole, and if you break it into 10,000 pieces, each has a north pole and a south pole. There is
no way
that you could end up with only a magnetic north pole in one hand and only a magnetic south pole in the other hand. However, if you have an object which is electrically charged (say, positively charged) and you break it into two pieces, both pieces can be positively charged.

Then things get really interesting. The third equation is Faraday’s law, which describes how changing magnetic fields produce electric fields. You can see how this equation serves as the theoretical foundation of the electric generators I talked about earlier. The last equation is Ampère’s law, which Maxwell modified in important ways. Ampère’s original law showed that an electric current generated a magnetic field. But by the time he was done with it, Maxwell had added a refinement, that a changing electric field creates a magnetic field.

By playing around with the four equations, Maxwell predicted the existence of electromagnetic waves traveling through empty space. What’s more, he could even calculate the speed of these waves. The truly shocking result was that their speed was the same as the speed of light. In other words, he concluded, light itself had to be an electromagnetic wave!

These scientists—Ampère, Faraday, and Maxwell—knew they were on the brink of a total revolution. Researchers had been trying to understand electricity in a serious way for a century, but now these guys were constantly breaking new ground. I sometimes wonder how they managed to sleep at night.

Maxwell’s equations, because of what they brought together in 1861, were really the crowning achievement of nineteenth-century physics, most certainly for all physics between Newton and Einstein. And like all profound discoveries, they pointed the way for further efforts to try to unify fundamental scientific theories.

Ever since Maxwell, physicists have spent incalculable efforts trying to develop a single unified theory of nature’s four fundamental forces:
the electromagnetic, strong nuclear, weak nuclear, and gravitational forces. Albert Einstein spent the last thirty years of his life in a failed effort to combine electromagnetism and gravity in what became known as a unified field theory.

The search for unification goes on. Abdus Salam, Sheldon Glashow, and Steven Weinberg won the Nobel Prize in 1979 for unifying electromagnetism and the weak nuclear force into what’s known as the electro-weak force. Many physicists are trying to unify the electroweak force and the strong nuclear force into what is called a grand unified theory, or GUT, for short. Achieving that level of unification would be a staggering accomplishment, on a par with Maxwell’s. And if, somehow, somewhere, a physicist ever manages to combine gravity with GUT to create what many call a theory of everything—well, that will be the holiest of Holy Grails in physics. Unification is a powerful dream.

That’s why, in my Electricity and Magnetism course, when we finally see all of Maxwell’s equations in their full glory and simplicity, I project them all around in the lecture hall and I celebrate this important milestone with the students by handing out flowers. If you can handle a little suspense, you will read more about this in
chapter 15
.

CHAPTER 9

Energy Conservation—
Plus ça change…

O
ne of the most popular demonstrations I’ve done through the years involves risking my life by putting my head directly in the path of a wrecking ball—a mini version of a wrecking ball, it must be said, but one that could easily kill me, I assure you. Whereas the wrecking balls used by demolition crews might be made from a bob, or spherical weight, of about a thousand kilos, I construct mine with a 15-kilo bob—about 33 pounds. Standing at one side of the lecture hall, with my head backed up against the wall, I hold the bob in my hands, snug up to my chin. When releasing it I must be extremely careful not to give it any kind of a push, not even a tiny little bit of a shove. Any push at all and it will surely injure me—or, as I say, possibly even kill me. I ask my students not to distract me, to make no noise, and even to stop breathing for a while—if not, I say, this could be my last lecture.

I have to confess that every time I perform this demonstration, I feel an adrenaline rush as the ball comes swinging back my way; as sure as I am that the physics will save me, it is always unnerving to stand there while it comes flying up to within a whisker of my chin. Instinctively I
clench my teeth. And the truth is, I always close my eyes too! What, you may ask, what possesses me to perform this demonstration? My utter confidence in one of the most important concepts in all of physics—the law of the conservation of energy.

One of the most remarkable features of our world is that one form of energy can be converted into another form, and then into another and another, and even converted back to the original. Energy can be transformed but never lost, and never gained. In fact, this transformation happens all the time. All civilizations, not only ours but even the least technologically sophisticated, depend on this process, in many variations. This is, most obviously, what eating does for us; converting the chemical energy of food, mostly stored in carbon, into a compound called adenosine triphosphate (ATP), which stores the energy our cells can use to do different kinds of work. It’s what happens when we light a campfire, converting the chemical energy stored in wood or charcoal (the carbon in each combines with oxygen) into heat and carbon dioxide.

It’s what drives an arrow through the air once it’s been shot from a bow, converting the potential energy, built up when you pull the bowstring back into kinetic energy, propelling the arrow forward. In a gun, it’s the conversion of chemical energy from the gunpowder into the kinetic energy of rapidly expanding gas that propels bullets out of the barrel. When you ride a bicycle, the energy that pushes the pedals began as the chemical energy of your breakfast or lunch, which your body converted into a different form of chemical energy (ATP). Your muscles then use that chemical energy, converting some of it into mechanical energy, in order to contract and release your muscles, enabling you to push the pedals. The chemical energy stored in your car battery is converted to electric energy when you turn the ignition key. Some electric energy goes to the cylinders, where it ignites the gasoline mixture, releasing the chemical energy released by the gasoline as it burns. That energy is then converted into heat, which increases the pressure of the gas in the cylinder, which in turn pushes the pistons. These turn the crankshaft,
and the transmission sends the energy to the wheels, making them turn. Through this remarkable process the chemical energy of the gasoline is harnessed to allow us to drive.

Hybrid cars rely in part on this process in reverse. They convert some of the kinetic energy of a car—when you step on the brakes—into electric energy that is stored in a battery and can run an electric motor. In an oil-fired furnace, the chemical energy of the oil is converted into heat, which raises the temperature of water in the heating system, which a pump then forces through radiators. In neon lights, the kinetic energy of electric charges moving through a neon gas tube is converted into visible light.

The applications are seemingly limitless. In nuclear reactors, the nuclear energy that is stored in uranium or plutonium nuclei is converted into heat, which turns water into steam, which turns turbines, which create electricity. Chemical energy stored in fossil fuels—not only oil and gasoline but also coal and natural gas—is converted into heat, and, in the case of a power plant, is ultimately converted to electrical energy.

You can witness the wonders of energy conversion easily by making a battery. There are lots of different kinds of batteries, from those in your conventional or hybrid car to those powering your wireless computer mouse and cell phone. Believe it or not, but you can make a battery from a potato, a penny, a galvanized nail, and two pieces of copper wire (each about 6 inches long, with a half-inch of insulation scraped off at each end). Put the nail most of the way into the potato at one end, cut a slit at the other end for the penny, and put the penny into the slit. Hold the end of one piece of wire on the nail (or wrap it around the nail head); hold the other piece of wire on the penny or slide it into the slit so it touches the penny. Then touch the free ends of the wires to the little leads of a Christmas tree light. It should flicker a little bit. Congratulations! You can see dozens of these contraptions on YouTube—why not give it a try?

Clearly, conversions of energy are going on around us all of the time,
but some of them are more obvious than others. One of the most counterintuitive types is that of what we call gravitational potential energy. Though we don’t generally think of static objects as having energy, they do; in some cases quite a bit of it. Because gravity is always trying to pull objects down toward the center of the Earth, every object that you drop from a certain height will pick up speed. In doing so, it will lose gravitational potential energy but it will gain kinetic energy—no energy was lost and none was created; it’s a zero sum game! If an object of mass
m
falls down over a vertical distance
h
, its potential energy decreases by an amount
mgh
(
g
is the gravitational acceleration, which is about 9.8 meters per second per second), but its kinetic energy will increase by the same amount. If you move the object upward over a vertical distance
h
, its gravitational potential energy will increase by an amount
mgh
, and you will have to produce that energy (you will have to do work).

If a book with a mass of 1 kilogram (2.2 pounds) is on a shelf 2 meters (about 6.5 feet) above the floor, then, when it falls to the floor, its gravitational potential energy will decrease by 1 × 9.8 × 2 = 19.6 joules but its kinetic energy will be 19.6 joules when it hits the floor.