Electromagnetic Field

A Charge and Its Field

Rub a balloon on your hair and it clings to the wall. Rubbing has moved charge from your hair onto the balloon, leaving it with a little extra negative charge. Whether electrons, charged molecules or specks of material make the trip is still being studied. Charge comes in two kinds, positive and negative. Like kinds push each other apart, and opposite kinds pull together. Each charge fills the space round it with an electric field, and a second charge anywhere in that field is pushed or pulled by the field where it sits. The wall has no extra charge. The balloon’s field shifts the charge in the wall’s atoms very slightly, the positive part toward the balloon and the negative part away, and the nearer charge pulls harder than the farther one pushes.

The push weakens with distance, as the square of it: twice as far, a quarter as strong. Gravity weakens the same way, but it only ever pulls, and it is far weaker. Between two protons, the electric push is about 10³⁶ times their gravity.

So why don’t whole objects push and pull each other with such strength, and why does feeble gravity rule the sky? Because the two kinds of charge cancel. Every atom holds as much negative charge in its electrons as positive charge in its nucleus, and experiments find the electron’s and the proton’s charges equal and opposite to better than one part in 10²¹. Inside each atom, the full force binds the electrons to the nucleus. Between atoms only what is left over acts, and it joins atoms into molecules. It does not simply push your hand back from a table, as two like charges would: atoms are neutral, so as they approach, the push between their electron clouds is nearly cancelled by each cloud’s pull on the other atom’s nucleus. The push comes only once the clouds begin to overlap. A rule of quantum physics, that no two electrons can share one state, then forces the squeezed electrons into patterns that cost far more energy, and leaves the nuclei less shielded from each other’s push. The rule adds no force of its own: the push that holds the atoms apart is electric, and the rule is what makes it so stiff.

A Current Turns a Compass

Hold a wire carrying a current over a compass, and the needle swings round to stand across the wire. Charge on the move makes a magnetic field. Its lines run in circles round the wire, with no start and no end, and reversing the current turns every needle round. Two wires carrying currents the same way pull on each other, and opposite ways push apart, with no magnet anywhere.

Why should moving charge make a different kind of force? Because it is not a different kind. The electrons in a wire drift along at less than a millimeter a second, while the metal’s positive ions stay put, and the two charges cancel. Seen by a charge moving alongside the wire at the electrons’ pace, the ions are the ones moving, and relativity crowds them very slightly closer, while the electrons, now still, spread very slightly apart. The wire no longer quite cancels, and that sliver of an enormous electric force is the magnetic force. So a magnetic force acts on charges that move.

On a charge in flight, the magnetic force pushes sideways, across both its path and the field. It can turn the charge but never speed it up or slow it down. In the space round Earth, electric fields speed electrons up. They spiral down Earth’s field lines into rings of sky round the magnetic poles, where they light the aurora.

A fridge magnet has no current in it. Its pull comes from the electrons themselves. Each electron is a tiny magnet. It carries a fixed amount of real turning, called spin, though no ball is spinning, and in iron great numbers of spins line up together. A compass needle is such a magnet, and a magnetic field turns and pulls these tiny magnets as well as pushing on moving charge. Made by currents or by spins, every magnet has both a north and a south pole. Cut one in half and you get two magnets, each with both poles. No magnet with only one pole has ever been found.

People keep looking, because one would explain a striking pattern. Every particle’s charge is a whole multiple of one small basic amount, a third of the electron’s, and the electron’s and the proton’s are opposite to within the best measurements. A magnet with only one pole, a north with no south, would force this: if one existed anywhere in universe, charge everywhere would have to come in whole units. Theories that unite the forces at very high energies, proposed but not confirmed, explain whole units of charge too, and they predict such poles, made in the first instants of the Big Bang. Searches in rocks from the Moon, in cosmic rays and at the Large Hadron Collider have found none; a single possible sighting decades ago was never repeated.

A Moving Magnet Makes a Current

If a current makes a magnet, can a magnet make a current? It can, though not quite as one might expect. A magnet sitting still does nothing; only change does. Push a magnet into a coil of wire and a current flows. Hold it still and the current stops. Pull it out and the current flows the other way. A changing magnetic field always comes with an electric field that loops round it, and that field drives charge round the coil.

Almost all the world’s electricity, apart from what comes from solar panels, is made this way. In a power station, steam, water or wind turns magnets past coils, or coils past magnets. Only the motion between them matters: seen from the coil, the magnet’s changing field drives the charge round, and seen from the magnet, the coil’s charges are pushed as they are carried through its field. A transformer passes power from one coil to another with no wire between them: its iron core carries a changing magnetic field through both coils, and the energy crosses the space between them. An induction cooktop and a wireless phone charger work the same way.

The current a change drives always flows the way that pushes back against the change. Drop a strong magnet down a thick-walled copper pipe 60 centimeters long, and it takes about ten seconds to come out of the bottom. A coin dropped down the same pipe is through in a third of a second. A magnet does not stick to copper. The falling magnet’s field sweeps through the walls and drives currents round the pipe, and their field pushes back on the magnet. The better the metal conducts, the slower the magnet has to fall before the currents it drives can hold up its weight. The energy of the fall ends up as a faint warmth in the copper.

The Wave That Runs at Light Speed

A changing magnetic field comes with an electric field looping round it. The rule has a mirror image: a changing electric field comes with a magnetic field looping round it, even in empty space. Together the two rules allow something remarkable. An electric and a magnetic field can swing in step, rising and falling together, and run away from the charge that set them going, going on without it.

How fast it runs is set by two numbers measured on lab benches: how hard charges push each other, and how hard currents pull each other. The two can be compared by discharging a Leyden jar, a glass jar coated with metal foil that stores charge. One such comparison, put in today’s units, gave a speed of about 310,000 kilometers a second. By the same numbers, electric signals along a wire should travel at about this speed, the speed of light, and the field’s waves cross empty space at it too. So light is a ripple of the same field. Sparks make such waves as well. Radio, light and X-rays are all this one ripple, differing only in how often it repeats.

Where the Energy Flows

Here is a puzzle the field answers. Close a switch, and a lamp a few meters away lights almost at once. Yet the electrons in the copper creep along at a fraction of a millimeter a second, and one setting out from the battery would take hours to reach the lamp. So what carries the energy?

The field does. The battery leaves a tiny excess of charge on the surface of each wire, positive on one and negative on the other, which fills the space between them with an electric field, and the current wraps each wire in a magnetic field. Where the two fields cross, energy flows. It flows out of the battery, along through the space between and beside the wires, and into the lamp, where it becomes light and warmth. The wires guide the flow. The copper itself carries almost none of it, and the little that turns into the wire warms it.

A wall socket does the same with alternating current. Its electrons rock back and forth, fifty or sixty times a second, by less than a thousandth of a millimeter, and go nowhere at all. The energy still flows one way, from the power station to the lamp, through the field around the cable.

The Field Comes in Lumps

One more surprise: the field’s waves hand over energy only in whole lumps, called photons. Light of a given color carries its energy in steps of one size, and light dim enough lands on a screen in single dots. Sent one at a time toward a half-silvered mirror, each lump is found on one side or the other, never split between both. An atom takes and gives light in whole photons too. Its electrons sit in set wave patterns. It can absorb a lone photon only if the photon’s energy matches a step up to another pattern, or is enough to tear an electron free. In ordinary light two photons almost never join forces to lift it; that takes intense laser light. Lifted a step, the atom returns to its lowest pattern after a wait that differs every time, under two billionths of a second on average when light lifts hydrogen to its first step, and sends out a new photon of the same energy.

Quantum electrodynamics describes the field and its charges together, lumps and all. It works out the push between two electrons as a sum of terms, each drawn as a small diagram with photons passed between them. These “virtual” photons are steps in the calculation, not particles anyone could catch on the way. The sum works astonishingly well: its prediction for the magnetism of a single electron matches the measured value to about one part in a trillion. The test now hangs on how well the strength of the electric force itself is known, and the two best measurements of that strength disagree slightly, a gap still being chased.