Magnetism and Electromagnetism

Every magnet has a north pole and a south pole. Bring two magnets together and like poles repel, unlike poles attract. Cut a bar magnet in half and you don't get a lone north and a lone south: you get two smaller magnets, each with both poles. No one has ever found a single, isolated pole.

We picture the magnetic field with field lines. Outside a magnet they run from the north pole to the south pole; they never cross; and they're crowded together where the field is strong. Sprinkle iron filings on paper over a magnet and they line up along these lines. A small compass placed anywhere points along the line through that spot.

Only a few materials, mainly iron, nickel and cobalt and some of their alloys, are strongly attracted to magnets. They're called ferromagnetic. Inside them, tiny regions called domains act like mini-magnets. Usually the domains point every which way and cancel out; a magnet nearby lines them up, and the material becomes magnetized.

Earth behaves as if it had a huge bar magnet inside it. The field actually comes from currents of molten iron flowing in its outer core. At the surface the field is weak, roughly 25 to 65 microteslas (μT), but it's enough to turn a compass needle.

The north pole of a compass needle points toward the Arctic, and unlike poles attract, so the magnetic pole near the geographic North Pole is really a magnetic south pole. It also wanders, drifting tens of kilometers a year, which is why maps list the difference between true north and magnetic north. Earth's field also shields us by steering charged particles from the Sun toward the poles, where they light up the sky as auroras.

In 1820 Hans Christian Ørsted noticed that a compass needle moved when a current flowed in a nearby wire. Every electric current makes a magnetic field. Around a long straight wire the field lines are circles centered on the wire. To find their direction use the right-hand rule: point your right thumb along the current, and your fingers curl the way the field goes.

The field gets weaker with distance r from the wire: B = μ₀I ÷ (2πr), where μ₀ ≈ 4π × 10⁻⁷ T·m/A. Wind the wire into a coil, called a solenoid, and the fields of all the loops add up. Inside, the field is strong and nearly uniform; outside, it looks just like a bar magnet's. Put an iron core inside and the field gets hundreds of times stronger: you've made an electromagnet. More turns, more current or an iron core all make it stronger, and it switches off when the current stops. Electromagnets are used in scrapyard cranes, door locks, loudspeakers and MRI machines.

If a current makes a magnetic field, then a magnetic field should push on a current, and it does: a wire of length L carrying current I through a field B feels a force

F = BIL sin θ

where θ is the angle between the wire and the field. The force is biggest when the wire is at right angles to the field (sin 90° = 1) and zero when it runs along the field. Its direction is at right angles to both the current and the field; on a diagram you can find it with a right-hand rule (fingers along B, thumb along I, and the force comes out of your palm) or Fleming's left-hand rule.

A current is just moving charges, so a single charge q moving at speed v through a field also feels a force:

F = qvB sin θ

Because this force is always at right angles to the motion, it changes the charge's direction but not its speed. A charge moving across a uniform field goes round in a circle. That's how particle accelerators steer beams, and how mass spectrometers sort atoms by mass.

Put a loop of wire in a magnetic field and pass a current through it. The current goes one way along one side of the loop and the other way along the opposite side, so the two sides are pushed in opposite directions, up and down. The loop turns. In a DC motor, a split-ring commutator reverses the current every half turn so the loop keeps spinning the same way. Real motors use many turns of wire on an iron core and strong magnets or electromagnets. They turn electrical energy into motion in everything from phone vibrators to electric cars.

In 1831 Michael Faraday found the reverse of Ørsted's discovery: a changing magnetic field makes a current. Push a magnet into a coil and a meter connected to the coil flicks one way. Hold it still and nothing happens. Pull it out and the meter flicks the other way. Joseph Henry found the same effect in America at around the same time.

Faraday's law says the induced voltage depends on how fast the magnetic field through the coil changes, and on the number of turns. Move the magnet faster, use a stronger magnet or add more turns and you get more voltage. Lenz's law gives the direction: the induced current always makes a field that opposes the change that caused it. Energy is conserved: you have to do work to push the magnet in, and that work becomes electrical energy.

A generator is a motor run backward. Steam, wind or falling water turns a coil in a magnetic field (or a magnet inside a coil), and the constantly changing field induces a voltage that flips direction every half turn: alternating current (AC). In the US the grid alternates 60 times a second (60 Hz); in much of the world it's 50 Hz.

A transformer has two coils wound on the same iron core. AC in the primary coil makes a changing field in the core, which induces a voltage in the secondary coil. The voltages are in the same ratio as the numbers of turns:

V_s ÷ V_p = N_s ÷ N_p

A step-up transformer has more turns on the secondary; a step-down transformer has fewer. An ideal transformer doesn't create energy, so power in equals power out: V_pI_p = V_sI_s. Power companies step voltages up to hundreds of thousands of volts for long-distance lines, because a lower current loses less energy as heat in the wires, then step them down again near your home.

Lodestones, naturally magnetic rocks, were known in ancient Greece and China, and compasses were guiding ships by the 1100s. In 1600 the English physician William Gilbert published De Magnete, showing with a small magnetized sphere that Earth itself is a great magnet.

For two centuries electricity and magnetism seemed unrelated. Then in 1820 the Danish physicist Hans Christian Ørsted saw a compass needle swing beside a wire carrying current. Within months André-Marie Ampère in Paris showed that two parallel currents attract or repel each other. In 1821 Michael Faraday made a wire spin around a magnet, the first electric motor, and in 1831 he discovered electromagnetic induction. Joseph Henry built powerful electromagnets and found induction independently, and in 1834 Heinrich Lenz stated the rule for its direction.

James Clerk Maxwell then described electricity and magnetism with one set of equations. In 1865 they predicted electromagnetic waves traveling at the speed of light, and he concluded that light itself is one.