by Walter Lewin
If I were to take 6.5 billion atoms, roughly the same as the number of people on Earth, and line them up in a row, touching one another, I would have a line about 2 feet long. But even smaller than every atom, about ten thousand times smaller, is its nucleus, which contains positively charged protons and neutrons. The latter, as you might imagine from their name, are electrically neutral; they have no charge at all. Protons (Greek for “first one”) have about the same mass as the neutrons—the inconceivably small two-billionths of a billionth of a billionth (2 × 10–27) of a kilogram, approximately. So no matter how many protons and neutrons a nucleus has—and some have more than two hundred—it remains a real lightweight. And tiny: just about a trillionth of a centimeter in diameter.
Most important for understanding electricity, however, is that the proton has a positive charge. There’s no intrinsic reason for it to be called positive, but since Franklin, physicists have called the charge left on a glass rod after it’s been rubbed with silk positive, so protons are positive.
Even more important, it turns out, is the remainder of the atom, consisting of electrons—negatively charged particles that swarm around the nucleus in a cloud, at some distance by subatomic standards. If you hold a baseball in your hand, representing an atomic nucleus, the cloud of electrons around it would range as far as half a mile away. Clearly, most of the atom is empty space.
The negative charge of an electron is equal in strength to the positive charge of the proton. As a result, atoms and molecules that have the same number of protons and electrons are electrically neutral. When they are not neutral, when they have either an excess or deficit of electrons, we call them ions. Plasmas, as we discussed in chapter 6, are gases partially or fully ionized. Most of the atoms and molecules we deal with on Earth are electrically neutral. In pure water at room temperature only 1 in 10 million molecules are ionized.
As a consequence of Franklin’s convention, when some objects have an overabundance of electrons, we say that they are negatively charged, and when they have a deficit of electrons, we say they have a positive charge. When you rub glass with a piece of silk you “rub off” (sort of) lots of electrons, so the glass ends up with a positive charge. When you rub amber or hard rubber with the same piece of silk, they collect electrons and develop a negative charge.
In most metals large numbers of electrons have escaped their atoms altogether and are more or less freely wandering around between atoms. These electrons are particularly susceptible to an external charge, either positive or negative, and when such a charge is applied, they move toward or away from it—thus creating electric current. I have a lot more to say about current, but for the time being I’ll just point out that we call these materials conductors, because they easily conduct (allow the movement of) charged particles, which in this case means electrons. (Ions can also create electric currents but not in solids, and thus not in metals.)
I love the idea of electrons just ready to play, ready to move, ready to respond to positive or negative charges. In nonconductors, there’s very little action of this sort; all the electrons are well fixed to their individual atoms. But that doesn’t mean we can’t have some fun with nonconductors—especially your garden-variety, rubber, nonconducting balloon.
You can demonstrate everything I’m talking about here by supplying yourself with a little pack of uninflated rubber balloons (thinner ones work better, like the ones you can twist into animals). Since most of you don’t have glass rods sitting around, I had hoped that a water glass or wine bottle or even a lightbulb might substitute, but despite my best efforts, they don’t. So why not try a large plastic or hard rubber comb? It will also be helpful to have a piece of silk, maybe an old tie or scarf, or a Hawaiian shirt your significant other has been trying to get you to throw out. But if you don’t mind getting your hair mussed—for the cause of science, who would mind?—you can make use of your own hair. And you’ll need to tear up some paper into, say, a few dozen or so pieces. The number doesn’t matter, but they should be small, about the size of a dime or penny.
Like all static electricity experiments, these work a lot better in winter (or in afternoon desert air), when the air is dry rather than moist. Why? Because air itself is not a conductor—in fact, it’s a pretty good insulator. However, if there is water in the air, charge can bleed away for complicated reasons which we will not discuss. Instead of allowing charge to build up on a rod or cloth or balloon, or your hair, humid air gradually bleeds charge away. That’s why you only have a problem getting shocked on doorknobs when the air is really dry.
Invisible Induction
Assemble all your materials, and get ready to experience some of the wonders of electricity. First charge up your comb by rubbing it hard on your hair, making sure your hair is very dry, or rubbing it with the piece of silk. We know from the triboelectric series that the comb will pick up negative charge. Now, stop for a moment and think about what’s going to happen as you bring the comb close to the pile of paper bits, and why. I could certainly understand if you say “nothing at all.”
Then put the comb a few inches above your little mound of paper pieces. Slowly lower the comb and watch what happens. Amazing, isn’t it? Try it again—it’s no accident. Some of the bits of paper jump up to your comb, some stick to it for a bit and fall back down, and some stay fast. In fact, if you play around with the comb and the paper a bit, you can make the pieces of paper stand on edge, and even dance on the surface. What on earth is going on? Why do some pieces of paper stick to the comb, while others jump up, touch, and fall right back down?
These are excellent questions, with very cool answers. Here’s what happens. The negative charge on the comb repels the electrons in the paper atoms so that, even though they’re not free, they spend just a little more time on the far side of their atoms. When they do so, the sides of the atoms nearest the comb are just a tiny bit more positively charged than they had been before. So, the positive-leaning edge or side of the paper is attracted to the negative charge on the comb, and the very lightweight paper jumps up toward the comb. Why does their attractive force win out over the repulsive force between the comb’s negative charge and the electrons in the paper? It’s because the strength of electrical repulsion—and attraction—is proportional to the strength of the charges, but inversely proportional to the square of the distance between them. We call this Coulomb’s law, named after the French physicist Charles-Augustin de Coulomb, who made this important discovery, and you will notice its astonishing similarity to Newton’s law of universal gravitation. Note that we also call the basic unit of charge the coulomb, and the positive unit of charge is +1 coulomb (about 6 × 1018 protons), while the negative charge is –1 coulomb (about 6 × 1018 electrons).
Coulomb’s law tells us that even a very small difference in the distance between the positive charges and the negative charges can have a large effect. Or put differently, the attractive force of the nearer charges overpowers the repelling force of the more distant charges.
We call this entire process induction, since what we are doing when we bring a charged object toward a neutral one is inducing charge on the near and far sides of the neutral object, creating a kind of charge polarization in the pieces of paper. You can see several versions of this little demonstration in my lecture for kids and their parents called “The Wonders of Electricity and Magnetism” on MIT World, which you can find here: http://mitworld.mit.edu/video/319.
As for why some bits of paper fall right back down while some stay stuck, this is also interesting. When a piece of paper touches the comb, some of the excess electrons on the comb move to the paper. When that happens, there still may be an attractive electric force between the comb and the piece of paper, but it may not be large enough anymore to counter the force of gravity, and thus the piece of paper will fall down. If the charge transfer is high, the electric force may even become repelling, in which case both the force of gravity and the electric force will accelerate the piece of paper down
ward.
Now blow up a balloon, knot the end so it stays blown up, and tie a string to the end. Find a place in your house where you can hang the balloon freely. From a hanging lamp, perhaps. Or you can put a weight of some kind on the string and let the balloon hang down from your kitchen table, about six inches to a foot. Charge the comb again by rubbing it vigorously with the silk or on your hair—remember, more rubbing produces a stronger charge. Very slowly, bring your comb close to the balloon. What do you think is going to happen?
Now try it. Also pretty weird, right? The balloon moves toward the comb. Just like with the paper, your comb produced some kind of separation of charge on the balloon (induction!). So what will happen when you move the comb farther away—and why? You know, intuitively, that the balloon will return to its vertical position. But now you know why, right? When the external influence disappears, the electrons no longer have any reason to hang out a little more on the far side of their respective atoms. Look what we were able to deduce just from this little bit of rubbing a comb and playing with little pieces of paper and a drugstore balloon!
Now blow up some more of the balloons. What happens when you rub one vigorously on your hair? That’s right. Your hair starts to do weird things. Why? Because in the triboelectric series human hair is way at the positive end, and a rubber balloon is on the seriously negative side. In other words, rubber picks up a lot of the electrons from your hair, leaving your hair charged positively. Since like charges repel, what else can your hair do when each strand has a positive charge and wants to get away from all the other like-charged hairs? Your strands of hair are repelling one another, making them stand up. This is of course also what happens when you pull a knit hat off of your head in winter. In rubbing your hair, the hat takes lots of electrons away, leaving the strands of your hair positively charged and aching to stand up.
Back to the balloons. So you’ve rubbed one vigorously on your hair (rubbing it on your polyester shirt may work even better). I think you know what I’m going to suggest, right? Put the balloon against the wall, or on your friend’s shirt. It sticks. Why? Here’s the key. When you rub the balloon, you charge it. When you hold the balloon against the wall, which is not much of a conductor, the electrons orbiting the atoms in the wall feel the repulsive force of the balloon’s negative charge and spend just a wee bit more time on the side of the atom farthest away from the balloon and a little bit less on the side closest to the balloon—that’s induction!
The surface of the wall, in other words, right where the balloon is touching it, will become slightly positively charged, and the negatively charged balloon will be attracted. This is a pretty amazing result. But why don’t the two charges—the positive and negative charges—just neutralize each other, with charges transferring, making the balloon immediately fall off? It’s a very good question. For one thing the rubber balloon has picked up some extra electrons. They don’t move around very easily in a nonconductor like rubber, so charges tend to stay put. Not only that, you’re not rubbing the balloon against the wall, making lots and lots of contact. It’s just sitting there, doing its attractive thing. But it’s also held there by friction. Remember the Rotor carnival ride back in chapter 3? Here the electric force plays the role played by the centripetal force of the Rotor. And the balloon can stay on the wall for some time, until the charge gradually leaks off the balloon, generally onto moisture in the air. (If your balloons don’t stick, the air is either too humid, making the air a better conductor, or your balloons might be too heavy—I suggested thin ones for just this reason.)
I have a ball sticking balloons on the kids who come to my public lectures. I have done this for years at kids’ birthday parties, and you can have great fun with it too!
Induction works for all kinds of objects, conductors as well as insulators. You could do the comb experiment with one of those helium-filled Aluminized Mylar balloons you can buy in grocery or dollar stores. As you bring the comb near the balloon, its free electrons tend to move away from the negatively charged comb, leaving positively charged ions nearer the comb, which then attract the balloon toward it.
Even though we can charge rubber balloons by rubbing them on our hair or shirt, rubber is, in fact, a nearly ideal insulator—which is why it’s used to coat conducting wires. The rubber keeps charge from leaking out of the wires into moist air or jumping to a nearby object—making sparks. After all, you don’t want sparks jumping around in flammable environments, like the walls of your house. Rubber can and does protect us from electricity all the time. What it cannot do, however, is protect us from the most powerful form of static electricity you know: lightning. For some reason people keep repeating the myth that rubber sneakers or rubber tires can protect us from lightning. I’m not sure why these ideas still have any currency, but you’re best off forgetting them immediately! A lightning bolt is so powerful that it doesn’t care one bit about a little bit of rubber. Now you may be safe if lightning hits your car—probably not, in reality—but it doesn’t have anything to do with the rubber tires. I’ll get to that a little later.
Electric Fields and Sparks
I said before that lightning was just a big spark, a complicated spark, but still a spark. But then what, you may ask, are sparks? OK, to understand sparks we need to understand something really important about electric charge. All electric charges produce invisible electric fields, just as all masses produce invisible gravitational fields. You can sense the electric fields when you bring oppositely charged objects close to each other and you see the attraction between them. Or, when you bring like-charged objects close and see the repelling force—you are seeing the effects of the electric field between the objects.
We measure the strength of that field in units of volts per meter. Frankly, it’s not easy to explain what a volt is, let alone volts per meter, but I’ll give it a try. The voltage of an object is a measure of what’s called its electric potential. We will assign a zero electric potential to the Earth. Thus the Earth has zero voltage. The voltage of a positively charged object is positive; it’s defined as the amount of energy I have to produce to bring the positive unit of charge (+1 coulomb—which is the charge of about 6 × 1018 protons) from Earth or from any conducting object connected with the Earth (e.g., the water faucets in your house) to that object. Why do I have to produce energy to move that unit of charge? Well, recall that if that object is positively charged, it will repel the positive unit charge. Thus I have to generate energy (in physics we say I have to do work) to overcome that repelling force. The unit of energy is the joule. If I have to generate 1 joule’s worth of energy, then the electric potential of that object is +1 volt. If I have to generate 1,000 joules, then the electric potential is +1,000 volts. (For the definition of 1 joule, see chapter 9.)
What if the object is negatively charged? Then its electric potential is negative and it is defined as the energy I have to produce to move the negative unit of charge (–1 coulomb—about 6 × 1018 electrons) from the Earth to that object. If that amount of energy is 150 joules, then the electric potential of the object is –150 volts.
The volt is therefore the unit of electric potential. It is named after the Italian physicist Alessandro Volta, who in 1800 developed the first electric cell, which we now call a battery. Note that a volt is not a unit of energy; it is a unit of energy per unit charge (joules/coulomb).
An electric current runs from a high electric potential to a lower one. How strong this current is depends on the difference in electric potential and on the electric resistance between the two objects. Insulators have a very high resistance; metals have a low resistance. The higher the voltage difference and the lower the resistance, the higher the resulting electric current. The potential difference between the two small slots in the electric wall outlets in the United States is 120 volts (it’s 220 volts in Europe); however, that current is also alternating (we’ll get to the matter of alternating current in the next chapter). We call the unit of current the ampere (amp), na
med after the French mathematician and physicist André-Marie Ampère. If a current in a wire is 1 amp, it means that everywhere through the wire a charge of 1 coulomb passes per second.
So what about sparks? How does all of this explain them? If you have scuffed your shoes a lot on the carpet, you may have built up an electric potential difference as high as about 30,000 volts between you and the Earth, or between you and the doorknob of a metal door 6 meters away from you. This is 30,000 volts over a distance of 6 meters, or 5,000 volts per meter. If you approach the doorknob, the potential difference between you and the doorknob will not change, but the distance will get smaller, thus the electric field strength will increase. Soon, as you are about to touch the doorknob, it will be 30,000 volts over a distance of about 1 centimeter. That’s about 3 million volts per meter.
At this high value of the electric field (in dry air at 1 atmosphere) there will be what we call an electric breakdown. Electrons will spontaneously jump into the 1-centimeter gap, and in doing so will ionize the air. This in turn creates more electrons making the leap, resulting in an avalanche, causing a spark! The electric current shoots through the air to your finger before you can touch the doorknob. I’ll bet you’re cringing a bit, remembering the last time you felt such a lovely little shock. The pain you feel from a spark occurs because the electric current causes your nerves to contract, quickly and unpleasantly.
What makes the noise, the crackle, when you get a shock? That’s easy. The electric current heats the air super quickly, which produces a little pressure wave, a sound wave, and that’s what we hear. But sparks also produce light—even though you may not see the light during the day, though sometimes you do. How the light is produced is a little more complicated. It results when the ions created in the air recombine with electrons in the air and emit some of the available energy as light. Even if you cannot see the light from sparks (because you aren’t in front of a mirror in a dark room), when you brush your hair in very dry weather you can hear the crackling noise they make.