For the Love of Physics (23 page)

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 × 10
¹⁸
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 × 10
¹⁸
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), named 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.

Just think, without even trying very hard, by brushing your hair or taking off that polyester shirt, you have created, at the ends of your hair, and on the surface of your shirt, electric fields of about
3 million volts per meter.
So, if you reach for a doorknob and feel a spark at, say, 3 millimeters, then the potential difference between you and the knob was of the order of 10,000 volts.

That may sound like a lot, but most static electricity isn’t dangerous at all, mainly because even with very high voltage, the current (the number of charges going through you in a given period of time) is tiny. If you don’t mind little jolts, you can experiment with shocks and have some fun—and demonstrate physics at the same time. However, never stick any metal in the electric outlets in your house. That can be very very dangerous—even life threatening!

Try charging yourself up by rubbing your skin with polyester (while wearing rubber-soled shoes or flip-flops, so the charge doesn’t leak to the floor). Turn off the light and then slowly move your finger closer and closer to a metal lamp or doorknob. Before they touch you ought to see a spark jump across the air between the metal and your finger. The more you charge yourself up, the greater the voltage difference you’ll create between you and the doorknob, so the stronger the spark will be, and the louder the noise.

One of my students was charging himself up all the time without meaning to. He reported that he had a polyester bathrobe that he only wore in the wintertime. This turned out to be an unfortunate choice, because every time he took the robe off, he charged himself up and then got a shock when he turned off his bedside lamp. It turns out that human skin is one of the most positive materials in the triboelectric series, and polyester is one of the most negative. This is why it’s best to wear a polyester shirt if you want to see the sparks flying in front of a mirror in a dark room, but not a polyester bathrobe.

To demonstrate in a rather dramatic (and very funny) way how people can get charged, I invite a student who is wearing a polyester jacket to sit on a plastic chair in front of the class (plastic is an excellent insulator). Then, while standing on a glass plate to insulate myself from the floor, I start beating the student with cat fur. Amid loud laughter of the students, the beating goes on for about half a minute. Because of the conservation of charge, the student and I will get oppositely charged, and an electric potential difference will build up between us. I show my class that I have one end of a neon flash tube in my hand. We then turn off the lights in the lecture hall, and in complete darkness I touch the student with the other end of the tube, and there is a light flash (we both feel an electric shock)! The potential difference between the student and me must have been at least 30,000 volts. The current flowing through the neon flash tube and through us discharged both of us. The demonstration is hilarious and very effective.

“Professor Beats Student” on YouTube shows the beating part of my lecture:
www.organic-chemistry.com/videos-professor-beats-student-%5BP4XZ-hMHNuc%5D.cfm
.

To further explore the mysteries of electric potential I use a wonderful device known as the Van de Graaff generator, which appears to be a simple metal sphere mounted on a cylindrical column. In fact, it’s an ingenious device for producing enormous electric potentials. The one in my classroom generally tops out at about 300,000 volts—but they can go much higher. If you look at the first six lectures on the web in my
electricity and magnetism course (8.02), you will see some of the hilarious demonstrations I can do with the Van de Graaff. You’ll see me create electric field breakdown—huge sparks between the large dome of the Van de Graaff and a smaller grounded ball (thus connected with the Earth). You’ll see the power of an invisible electric field to light a fluorescent tube, and you’ll see that when the tube turns perpendicular to the field it turns “off.” You’ll even see that in complete darkness I (briefly) touch one end of the tube, making a circuit with the ground, and the light glows even more strongly. I cry out a little bit, because the shock is actually pretty substantial, even though it’s not in the least bit dangerous. And if you want a real surprise (along with my students), see what happens at the end of lecture 6, as I demonstrate Napoleon’s truly shocking method of testing for swamp gas. The URL is:
http://ocw.mit.edu/courses/physics/8-02-electricity-and-magnetism-spring-2002/video-lectures/
.

Fortunately, high voltage alone won’t kill or even injure you. What counts is the current that goes through your body. Current is the amount of charge per unit of time, and as said before, we measure it in amperes. It’s current that can really hurt or kill you, especially if it’s continuous. Why is current dangerous? Most simply, because charges moving through your body cause your muscles to contract. At extremely low levels, electric currents make it possible for your muscles to contract, or “fire,” which is vital to getting around in life. But at high levels, it causes your muscles and nerves to contract so much that they twitch uncontrollably, and painfully. At even higher levels, it causes your heart to stop beating.

It is for these reasons that one of the darker sides of the history of electricity and the human body is the use of electricity for torture—since it can cause unbearable pain—and death, of course, in the case of the electric chair. If you’ve seen the movie
Slumdog Millionaire
, you may remember the horrible torture scenes in the police station, in which the brutish police attach electrodes to the young Jamal, causing his body to twitch wildly.

At lower levels, current can actually be healthy. If you’ve ever had physical therapy for your back or shoulder, you may have had the experience of what the therapists call “electrical stimulation”—stim for short. They put conducting pads connected to an electrical power source on the affected muscle and gradually increase the current. You have the odd sensation of feeling your muscles contract and release without your doing anything at all.

Electricity is also used in more dramatic healing efforts. You’ve all seen the TV shows where someone uses the electric pads, known as defibrillators, to try to regularize the heartbeat of a patient in cardiac distress. At one point in my own heart surgery last year, when I went into cardiac arrest, the doctors used defibrillators to get my heart beating again—and it worked! Without defibrillators,
For the Love of Physics
would never have seen the light of day.

People disagree about the exact amount of current that’s lethal, for obvious reasons: there’s not too much experimenting with dangerous levels. And there’s a big difference as to whether the current passes through one of your hands, for instance, or whether it goes through your brain or heart. Your hand might just burn. But pretty much everyone agrees that anything more than a tenth of an ampere, even for less than a second, can be fatal if it goes through your heart. Electric chairs used varied amounts, apparently; around 2,000 volts and from 5 to 12 amperes.

Remember when you were told as a kid not to put a fork or knife into a toaster in order to pull a piece of toast out, because you might electrocute yourself? Is that really true? Well, I just looked at the ratings of three appliances in my house: a radio (0.5 amp), my toaster (7 amps), and my espresso machine (7 amps). You can find these on a label on the bottom of most appliances. Some don’t have the amperage, but you can always calculate it by dividing the wattage, the appliance’s power, by the voltage, usually 120 in the United States. Most of the circuit breakers in my home are rated at between 15 and 20 amps. Whether your 120-volt appliances draw 1 or 10 amps is not really what matters. What matters is that you have to stay away from accidentally causing a short circuit and, above
all, from accidentally touching with a metal object the 120 volts; if you did this shortly after you had taken a shower, it could kill you. So what does all this information add up to? Just this: when your mother told you not to put a knife into a toaster while it was plugged in, she was
right.
If you ever want to repair any of your electric appliances, make sure you unplug them first. Never forget that current can be very
dangerous.

Divine Sparks

Of course, one of the most dangerous kinds of current is lightning, which is also one of the most remarkable of all electrical phenomena. It’s powerful, not completely predictable, much misunderstood, and mysterious, all at once. In mythologies from the Greek to the Mayan, lightning bolts have been either symbols of divine beings or weapons wielded by them. And no wonder. On average, there are about 16 million thunderstorms on Earth every year, more than 43,000 every day, roughly 1,800 every hour of the day, producing about 100 lightning flashes every second, or more than
8 million
lightning flashes every day, scattered around our planet.