Biographies & Memoirs

Chapter 6

Einstein’s Most Fascinating Subject

In This Chapter

bullet Exploring electricity

bullet Understanding the basics of magnetism

bullet Connecting electricity and magnetism

bullet Understanding Maxwell’s contributions to electromagnetism

bullet Seeing how theories alter reality

“C onvert Magnetism into Electricity” — so wrote self-taught English scientist Michael Faraday in his lab book in the early 1800s. His work, and that of James Clerk Maxwell, made possible this conversion and produced the theory of electromagnetism.

Einstein considered this theory to be the “most fascinating subject” and skipped classes in college to read the original papers where the theory was presented. By the time Einstein graduated from college, he was an expert in this field, which was considered then to be at the frontier of physics. (He would later discover an inconsistency between electromagnetism and Isaac Newton’s idea of absolute time and, to resolve it, introduce his theory of relativity.)

In this chapter, I show you the theories that Einstein read about in those early papers on electromagnetism. I also explain how those theories helped shape Einstein’s (and our) understanding of the universe we live in.

Bringing Invisible Forces to Light

Newton’s mechanics (see Chapter 4) took center stage in physics until the mid-19th century. Scientists developed elegant mathematical versions of Newtonian mechanics. Armed with these powerful mathematical techniques, John Adams in England and Urbain Jean Joseph Le Verrier in France showed that small deviations in the orbit of Uranus were due to the existence of a planet orbiting beyond all the known planets. Neptune, the new planet, was discovered within a degree of where Adams and Le Verrier said it was going to be.

Successes like this made laypeople take an interest in science. They were excited to see that you could predict the existence of a planet by doing calculations on a piece of paper, using a scientific theory.

Other branches of physics, like optics, electricity, magnetism, and the studies on the nature of matter, continued developing at a much slower pace, away from the limelight. Luckily for Einstein, all of these branches reached maturity by the time he was in college. The most mature was electromagnetism, the very successful marriage between electricity and magnetism that had just been completed.

But Einstein’s favorite subject wasn’t just a 19th-century invention; it actually started with the ancient Greeks. In the next section, I tell you how their ideas developed into electromagnetism.

Feeling the sparks

Electricity and magnetism had been known from antiquity. The Greeks discovered that amber, a beautiful golden gem that’s still used in jewelry, attracted seeds or feathers when rubbed with cloth. They called amber elektron. They also knew that lodestone, or magnetite, attracted iron.

The body of knowledge about electricity and magnetism stayed fairly stagnant until the end of the 16th century when William Gilbert, the court physician to Queen Elizabeth I and a contemporary of Galileo and Johannes Kepler, began carefully designed experiments with magnets. He also investigated the attractive properties of amber and coined the word electric for anything that attracts like amber. He published his work in a large book called The Magnet.

In spite of Gilbert’s work, electricity and magnetism still remained curiosities — stuff used to entertain people at parties. Electric shows with sparks and tricks with magnets were not yet worth serious study.

The primary difficulty with understanding electricity and magnetism is that the sources of the attraction and repulsion of magnets and of electrified bodies aren’t visible. (By contrast, in mechanics you can see objects moving faster or slower, speeding up or colliding. You can measure the masses, clock the motion of objects, and observe their collisions.)

What’s the nature of these invisible forces? What makes amber attract pieces of straw? Why does a magnet attract iron regardless of which side of the magnet you use, when it either attracts or repels other magnets depending on which side you use? Studying electricity and magnetism seriously wasn’t easy. Fortunately, a few people persevered.

Discovering opposing forces

One such scientist was Ben Franklin, America’s renaissance man. He was aware of experiments done in France by the scientist Charles du Fay, who rubbed a glass rod with silk and then used it to touch a gold leaf (see Figure 6-1). The leaf was attracted to the glass rod before the rod touched it but moved away from it after touching. Du Fay thought that there were two kinds of electricity. He also thought that if two objects had the same kind, they would move away from each other, whereas if they had different kinds, they would move toward each other.

Figure 6-1: A gold leaf is attracted to a glass rod that you rub with silk — until the leaf touches the rod.

Figure 6-1: A gold leaf is attracted to a glass rod that you rub with silk — until the leaf touches the rod.

You can do a similar experiment at home. Simply take any plastic rod and rub it with silk. Instead of a gold foil, which is not easy to come by, cut a small strip of aluminum foil.


Franklin conducted similar experiments, as well as experiments with lightning, and saw that one kind of electricity could be neutralized by the other. He proposed that there was only one kind of electricity and that objects usually had a normal amount of it. Placing the objects together would allow some electricity to pass from one to the other.

After the transfer of electricity, Franklin thought that one of the objects would be left with an excess of electricity, which he indicated with a positive sign, while the other would be left with a deficiency, which he indicated with a negative sign.

In the experiments with the glass rod, which one was positive and which one was negative? Franklin had no way of knowing. He guessed that rubbing the glass rod with silk transferred electricity to the rod, leaving the rod positive and the silk negative (see Figure 6-2). He guessed wrong.

Figure 6-2: If you rub a glass rod with silk and then move them apart, the silk gains negative electricity and the glass positive.

Figure 6-2: If you rub a glass rod with silk and then move them apart, the silk gains negative electricity and the glass positive.

In the 20th century, scientists discovered that the carriers of electricity, or electric charge as we now call it, are electrons, which in Franklin’s convention are negatively charged. Rubbing glass with silk transfers these negative electrons from the rod to the silk, which leaves molecules in the glass lacking electrons.

The silk ends up with an excess of electrons and becomes negatively charged. The glass ends up with a deficiency of these negative electrons, which creates a charge imbalance in some of the oxygen and silicon atoms that make up the glass molecules. Normally, atoms are electrically neutral. As I explain in Chapter 15, atoms have a core of positive charges and a cloud of negative electrons, and these charges balance out. If you remove one electron from an atom, the atom is left with a net positive charge. In the case of rubbing silk on a glass rod, the rod ends up positively charged.

Typically, if you rub a glass rod with silk a couple of times, you transfer about a billion electrons from the glass to the silk. That sounds like a large number, but even if you rub vigorously, you can expect to remove electrons from only about one in a million atoms (if you have the best possible conditions).


Franklin thought that the positive charges were the ones transferred. We now know that the negatively charged electrons transfer instead. But we still use Franklin’s convention of positive and negative signs. Using Franklin’s convention, we can say that two positive or two negative charges repel each other, while a negative charge and a positive charge attract each other (see Figure 6-3).

Figure 6-3: Two positive or two negative charges repel each other. A negative and a positive charge attract each other.

Figure 6-3: Two positive or two negative charges repel each other. A negative and a positive charge attract each other.

Identifying Forces and Fields

Franklin taught us that electric charges attract or repel each other depending on their signs. But what is the nature of that attraction or repulsion? What is the force that makes them respond to the presence of the others?

There are two ways to look at this phenomenon, and both date back to the time before Einstein. One is the idea of the force acting between the charges that makes them move toward or away from each other. The second — the idea of fields — is more subtle but much more powerful.

Studying electric force

Before Franklin and Du Fay came onto the scene, Newton had already discovered that any two objects in the universe attract each other with a force that depends on the product of the objects’ masses, as well as the square of their distance. As I explain in Chapter 4, this is Newton’s powerful universal law of gravitation.


Newton’s universal law of gravitation actually depends on the inverse of the square of the distance separating the two objects. The inverse of any number is 1 divided by the number. The universal law is then called an inverse square law (see the sidebar “Inverse square laws”).

Franklin asked himself if the force between charges was also an inverse square law. But this force would have to be of two kinds, one attracting and the other one repelling. He asked his friend Joseph Priestley in England to look into this idea.

Priestley thought about the similarities between the electrical and gravitational cases, conducted some thought experiments, and proposed that this force was an inverse square law. Two years later, Charles Augustin de Coulomb, a French scientist, came up with a very clever method to measure this force and confirmed Franklin’s and Priestley’s insight (see the sidebar “Coulomb’s torsion balance”).


Like the gravitational force, the electric force between two charged objects depends on the inverse of the square of the distance. It also depends on the product of the charges of the two objects. Because there are both negative and positive charges, the product of these charges can also be positive or negative. A positive force is the force between two like charges (two positive or two negative charges). This force is repulsive; it pushes the charges apart. A negative force is the one between two unlike charges. This force is attractive; it tries to bring the charges together.


Inverse square laws

An inverse square law, like the electric force or Newton’s universal law of gravitation, says that the strength of a force between objects decreases as the distance between the objects increases. Specifically, the strength of the force decreases in proportion to the square of the distance. For example, if you double the distance between objects, the force between them decreases to one-fourth of its original strength. If you triple the distance, the force decreases to one-ninth the original strength. And if you quadruple it, it decreases to one-sixteenth.


Defining electric fields

The second way to look at interaction between two electric charges is by using the idea of a field. The term electric field describes the property of the space around an electrically charged object. The presence of a charged object at some place changes or distortsthe space around it so that every other charge in this field feels a force of attraction or repulsion toward the original charge.


Consider the following example. Suppose that you won tickets to the Super Bowl and are happily waiting for the game to start when a big pop star scheduled to perform during the halftime show enters the stadium. Quickly, everyone in the stadium knows about her presence. Some people see the singer directly, while others hear it from those who saw her. Most people just guess that she’s there based on the unusual activity in the crowd and the knowledge that she is supposed to perform at halftime.


Coulomb’s torsion balance

Calculating the force of gravity based on Newton’s universal law of gravitation wasn’t too difficult, because the masses and distances can be measured relatively easily. Not so with electrical charges. You can’t even see them, so how are you going to measure how far apart they are or what their values (positive or negative) are?

French scientist Charles Augustin de Coulomb invented a device that measured the force needed to twist a pair of small electrically charged spheres. The two spheres were placed at the end of an electrically insulating rod held by a thin wire. As the charged spheres moved apart or closer together, depending on the sign of their charges, the wire became twisted. He calculated the repulsive force from the twisting angle and proved Priestley’s insight: The force was an inverse square force.

Coulomb then placed uncharged spheres into contact with the original ones, transferring fractions of the original charge. With this procedure, he showed that the force depended on the product of the charges. The electric force between two bodies is now called the Coulomb force.


This knowledge of the singer’s presence spreads through the stadium without everyone seeing her with their own eyes. The stadium then becomes a field, a region where the regular activity of the people waiting for a game changes as a result of the presence of a celebrity. This change affects everyone in the field. Their thoughts are focused momentarily on the singer, and her image pops into their minds.

Take a look at Figure 6-4. The electric field around a charge is represented by a set of lines. Because like charges repel each other and unlike charges attract, the field lines have arrows showing the direction that a small positive test charge would take if placed at each point. The field lines of a small positively charged sphere (on the left) point outward because the test charge always moves away from a positive charge. The field lines of a small negatively charged sphere (on the right) point inward because the test charge is attracted to it at every point where you place it.

If you place two small spheres with equal and opposite charges at a short distance from each other, their field lines bend and meet, as shown in Figure 6-5. The field lines always indicate the direction in which a positive charge will move if you place it in the field. A negative charge will move in the opposite direction.

Figure 6-4: The electric field in the space around a positive charge (left) and around a negative charge (right).

Figure 6-4: The electric field in the space around a positive charge (left) and around a negative charge (right).

Figure 6-5: The electric field near a positive and a negative charge that are close together.

Figure 6-5: The electric field near a positive and a negative charge that are close together.


There are many other fields in physics. The gravitational field around the Earth, for example, is the property of the space around our planet where any object feels the Earth’s gravitational attraction. Einstein used the gravitational field to show that what he called spacetime, the four-dimensional combination of space and time, is curved and that gravity is simply this curved spacetime. I explain what this means in Chapter 12.

Examining magnetic fields

Here is a field that you can see: If you sprinkle some iron filings on the back of a greeting card (or on any piece of heavy paper) and then place a small bar magnet under the card, you’ll observe the iron filings aligning along curved paths from one end of the magnet to another (see Figure 6-6). The filings are showing you the shape of the magnetic field around the magnet.

Figure 6-6: The shape of the magnetic field lines around a bar magnet.

Figure 6-6: The shape of the magnetic field lines around a bar magnet.

Wherever you place a magnet, the space around the magnet changes. Any other magnetized body in the region senses this change and experiences a force. Like the gravitational force, the magnetic force is an inverse square law.


As you know from handling small magnets, every magnet has two distinct sides, usually called the north and south magnetic poles. If you hold two magnets with their north poles facing each other, they repel each other. The same thing happens if the two south poles face each other. When you flip one of the magnets so that the north pole of one magnet faces the south pole of the other, the two magnets attract each other and you can make them stick together.

Sensing the Attraction Between Electricity and Magnetism

Electricity and magnetism seem to have a lot in common. Here’s how they’re similar:

bullet Two kinds of electric charges exist, positive and negative. Two kinds of magnetic poles exist, north and south.

bullet Like charges repel each other, and unlike charges attract. Like poles repel each other, and unlike poles attract.

bullet The electric force is an inverse square-type force, and so is the magnetic force.

bullet The electric field lines around two equal and opposite charges have the same shape as those formed by the north and south magnetic poles in a magnet.

But there are differences. Positive and negative charges exist in isolation, while magnetic forces exist only in pairs.


Splitting magnets

In 1931, the renowned English physicist Paul Dirac proposed that single magnetic poles or monopoles should exist to complete the symmetry between electricity and magnetism. If the two electrical charges existed separately, why couldn’t the same be true for the two magnetic poles?

Recent theories of particle physics and cosmology suggest that magnetic monopoles existed during the early universe. If they exist, they can’t be obtained by splitting a magnet in two. Doing so produces two complete magnets, each with its own north and south poles.


Failing a Demo, and Changing Science

Encouraged by the similarities between electricity and magnetism, scientists looked for the connection between the two. One good place to start was with the possibility of electric currents generating magnetic fields. (An electric current is nothing more than the motion of electric charges, usually through some metal wire. Electric currents can exist in a vacuum or in some nonmetals, but the most common ones exist in metals.) Time after time, scientists tried and failed to demonstrate the connection.

In 1819, one professor in Denmark, Hans Christian Oersted, set up a demonstration to show his students that in spite of their similarities, electric and magnetic fields were not related and that you couldn’t produce one from the other. He’d done this demonstration many times before. He laid wires on the table in front of him and passed a current through them. With a small magnetic compass, he showed his students that the compass needle always remained pointing north regardless of how close he placed the compass to the wires. When he finished, he picked up the compass and noticed that the needle twitched and pointed in a direction perpendicular to the wire (see Figure 6-7).

Professor Oersted continued experimenting. He reversed the current and saw that the compass needle reversed direction but remained perpendicular to the wire.


While trying to prove the opposite, Oersted accidentally proved that there was a connection, after all: Electric fields could generate magnetic fields. No one had noticed this connection before because they were all placing the compass right next to the wire, not above or below it. Oersted’s experiment was the first documented instance of a force acting in a direction that was perpendicular to the motion of a body (in this case, the electrons that make up the electric current in the wire).

Figure 6-7: Oersted discovered that a magnetic compass is deflected if placed directly above or below an electric wire carrying a current.

Figure 6-7: Oersted discovered that a magnetic compass is deflected if placed directly above or below an electric wire carrying a current.

If you look at Figure 6-8, you’ll get a better idea of Oersted’s discovery. If you place several compasses right next to a current-carrying wire lying on a table, the compasses all point north (top left). If you pick one up, so that its magnetic needle is perpendicular to the wire, that compass is deflected (top right). The figure at the bottom shows how the magnetic field wraps around the wire.

Figure 6-8: Oersted’s discovery of the connection between electricity and magnetism.

Figure 6-8: Oersted’s discovery of the connection between electricity and magnetism.

Oersted published his discovery in 1820. Within a few months, scientists all over Europe were trying to reproduce his discovery. The young French physicist André Marie Ampère was able to extend Oersted’s discovery, describing it mathematically and proving that all forms of magnetism are generated by small electric currents.


An electric current is nothing more than one or more electric charges moving across some space. Ampère’s law, as we call this discovery today, can be stated as follows:

A moving electric charge generates a magnetic field.


Sloppy experimenter

Hans Christian Oersted made the discovery of the connection between electricity and magnetism for which he became famous somewhat accidentally. He might not have been a meticulous experimenter. One of his students wrote that Oersted was “a man of genius but . . . he could not manipulate instruments.” If this description is true, his lack of skill as an experimenter might’ve helped him make his discovery. More skillful scientists probably turned the current off before taking apart the experiment and failed to see the movement of the compass


Creating a Current

Oersted and Ampère had shown that an electric current produced a magnetic field. The obvious question now was: Would a magnetic field produce an electric current? Many scientists were trying to answer this question when, in 1821, a self-taught English scientist named Michael Faraday headed for his lab with several ideas in mind.

At first, none of Faraday’s ideas worked, but nobody else’s did either. Faraday didn’t give up. He tried intermittently and unsuccessfully for ten years to show that a magnetic field could produce an electric current. Finally, in 1832, he wound an insulated copper wire around one side of an iron ring and connected the two ends of that wire to a battery (see Figure 6-9). He then wound a second insulated wire around the other side of the ring and monitored any currents that might be generated in this coil.

Figure 6-9: Faraday’s experiment.

Figure 6-9: Faraday’s experiment.

Faraday knew that the electric current in the first wire would produce a magnetic field. That was Ampère’s law. That was what Oersted had seen and what got everyone excited.

Faraday also expected the magnetic field created in the first coil to propagate through the iron ring all the way to the other side, where the separate coil was. That propagation of the magnetic field had already been proven.

What Faraday was looking for was for this magnetic field to produce a current in the separate wire coil. The second coil was not connected to a source of electricity and was insulated from the iron ring on which it was wound. Faraday connected his battery and checked to see if any current was flowing through his second wire. Nothing.

He kept trying. Still no current in the second loop. But he noticed that every time he connected or disconnected the battery, the current meter on the separate loop tweaked. He was puzzled. Was it perhaps the change in the magnetic field in the ring that made the current meter register? He then tried to change the current on the first loop to see if that was the case.

It worked. He had his discovery. Actually, he had one of the major discoveries of the century. He had produced electricity from magnetism.


So it was a changing magnetic field that generated a current. For the next several months, Faraday tried other ways to produce a current in an isolated wire. He showed that the iron ring wasn’t needed. A changing current in one coil generated a changing magnetic field that in turn produced a current in a second separate coil sitting nearby. Even a moving magnet did the trick, because the isolated coil sensed an approaching or receding field (see Figure 6-10).

Figure 6-10: If you move a magnet toward a metal ring, you can create a current in the ring.

Figure 6-10: If you move a magnet toward a metal ring, you can create a current in the ring.

Faraday’s induction law, as we call his discovery today, is stated as follows:

A changing magnetic field generates an electric current.


What’s this invention good for?

After discovering his law of induction, Michael Faraday invented the electric generator. When he was already a famous scientist, the British prime minister is said to have asked him what his invention was good for. Supposedly, Faraday told the prime minister that one day he could tax it.

This story is very likely fictional, but the statement ended up being true. An electric generator is nothing more than several loops of wire that are made to rotate inside a magnet. A paddlewheel turned by a waterfall or by a river can be the source of energy to move the wire loops. As the wire loops rotate, the magnetic field lines that thread through the loops change from none (when the loops are oriented along the field lines) to a maximum (when the loops are at right angles to the field lines). The changing magnetic field generates the electric current in the wire. You now use this current in your home. And you can bet that the current prime minister is taxing this utility.


The Great Scot: Appreciating Maxwell

The discoveries of Oersted, Ampère, and Faraday showed to the scientific world that electricity and magnetism were closely related. Faraday showed us the complete connection between the two. But because he had no grasp of mathematics, he couldn’t give us the complete picture. He couldn’t understand a word of Ampère’s highly mathematical papers. He had to go by the descriptions of Oersted’s experiments and presentations of Ampère’s papers at meetings.

Enter James Clerk Maxwell (1831–1879), a highly trained Scottish scientist with a remarkable mathematical ability. In his first two papers on electromagnetism, he came up with a mathematical model for Faraday’s induction law. When he applied his model, he noticed that in addition to reproducing Faraday’s law (where a changing magnetic field produces a changing electric current), the model suggested that a changing electric field would also produce a magnetic field. That was close to what Ampère had said.

Ampère had discovered that a moving charge produced a magnetic field. If you use Faraday’s idea of electric field, Ampère’s law actually says that the electric field of the moving charge produces a magnetic field. Maxwell’s model was more general than that. It said that any changing electric field produced a magnetic field. A changing electric field between two metal plates, for example, where no charge was moving, should produce a magnetic field.


Maxwell decided to modify and extend Ampère’s law to include this possibility. This extension (which we now call the Ampère–Maxwell law) says

A changing electric field produces a changing magnetic field.

With this extension, Maxwell had one of the major scientific discoveries of all time. His was the stroke of genius that unified electricity and magnetism into one single theory that we now call electromagnetism.

Creating T-shirt Equations

The marriage between electricity and magnetism was now complete. One field generates the other. And Maxwell put it all in mathematical form — Maxwell’s famous equations. Today, you can buy a T-shirt with these equations on it (and some people even think it looks cool).

What Maxwell did was to take the work of Coulomb, Ampère, Faraday, and others and put it together into a complete and beautiful theory. The whole story is described in four equations. (Trust me, you don’t want to see them; they’re an eyeful.) The first one is a more elegant version of Coulomb’s law and gives a relationship between an electric charge and its electric field. The second equation describes magnetic field lines and shows the differences with electric field lines.

The beauty comes in the last two equations. The third equation is Faraday’s law of induction, and the fourth is the Ampère–Maxwell law.

You’ve seen what these laws say and do. I’ll show you why they are beautiful.

According to the third equation, a changing magnetic field creates an electric field that’s also changing. But the fourth equation says that this changing electric field in turn produces a changing magnetic field. This last changing electric field now creates a new changing magnetic field. You get the idea. Back and forth with the two equations.


When you set up the first changing field (either one of the two — it doesn’t matter which comes first), the other one is created right away, and the whole thing takes on a life of its own. The two interlocked fields become one single electromagnetic field that begins to expand in space.

Maxwell combined his equations into a single one to show that this electromagnetic field moves through space like a wave at 288,000 kilometers per second (kps). That number was very close to the speed of light, which had been measured at the time to be 311,000 kps.

Nine years after Maxwell died, Heinrich Hertz used Maxwell’s theory to generate electromagnetic waves in his lab. Today, of course, you are surrounded by electromagnetic waves generated by your hometown radio stations, your remote controls, or your cellphone. These waves all travel at 300,000 kps, the value that scientists have measured for them (which is very close to what had been measured a century and a half ago when Maxwell was discovering them).

We also send these electromagnetic waves to our spacecraft on the surface of Mars with instructions to climb up that intriguing hill we’re able to see because of the electromagnetic waves that the craft sent us 20 minutes ago.

Pretty exciting stuff. No wonder Einstein cut classes to go read up on Maxwell’s theories.

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