Magnetism and Electromagnetism

Legend says a shepherd named Magnes, on the Greek hillside of Magnesia, found that the iron nails in his sandals and the iron tip of his stick stuck to a certain black rock. That rock was lodestone (magnetite, Fe₃O₄), a natural magnet, and the words 'magnet' and 'magnetism' come from that place. Today most magnets are artificial: bar magnets, horse-shoe magnets and magnetic needles made by magnetising iron, steel, cobalt, nickel or alloys such as alnico.

The space around a magnet in which its influence can be felt is its magnetic field. We cannot see it, but we map it with magnetic field lines: imagine the path a tiny, free North pole would follow if released in the field. Sprinkle iron filings on paper over a bar magnet, tap it, and the filings arrange themselves along these lines. The SI unit of magnetic field strength (B) is the tesla (T) (named after Nikola Tesla); the older CGS unit is the gauss, where 1 T = 10⁴ gauss. The unit of magnetic flux is the weber (Wb).

Field lines are an imagination, not real threads. They tell you two things only: direction (along the line) and strength (how crowded the lines are). A free N pole moves along the line away from N; a free S pole moves the opposite way.

Now the biggest magnet we live on. The Earth behaves like a giant bar magnet, with its magnetic axis tilted by about 11° from the axis of rotation. The field is produced by the slow flow of molten iron and nickel in the Earth's outer core. Here comes the famous puzzle: the North pole of a compass needle points to geographic north, and since unlike poles attract, the pole of the Earth-magnet lying near geographic north must be a magnetic South pole. That is why a freely suspended magnet settles in the north-south direction, and that is how mariners find direction with a compass.

The Earth's field extends far into space as the magnetosphere, a shield that deflects the charged particles of the solar wind. Some particles are trapped in two doughnut-shaped zones, the Van Allen radiation belts (discovered in 1958 by James Van Allen's team on Explorer 1): the inner belt holds mostly protons and the outer belt mostly electrons. Particles that leak in near the poles light up the sky as the auroras (Aurora Borealis in the north, Aurora Australis in the south). Mars, which lost its global magnetic field, has also lost most of its atmosphere to the solar wind, a standard example of why a magnetic field matters.

Hold a magnet near a steel spoon, an aluminium foil, a copper coin and a piece of wood. The spoon jumps to the magnet, the foil barely responds, and the coin and the wood seem to ignore it. In truth every substance responds to a magnetic field, only by very different amounts. Scientists therefore sort materials into three groups: diamagnetic, paramagnetic and ferromagnetic. The reason lies in the atoms. Electrons act like tiny magnets; in some atoms they cancel one another, in some they leave a weak net magnet, and in a few metals they line up in big groups called domains.

A ferromagnetic material loses its strong magnetism when heated above a particular temperature called the Curie temperature (about 770 °C for iron), after which it behaves like a paramagnetic material. This is why heating a magnet is one way to destroy it. Ferromagnetic materials are also classed by how stubbornly they keep their magnetism. Soft iron is magnetised easily and loses its magnetism easily, so it is used in electromagnets, transformer cores and motors. Steel and alloys like alnico (aluminium–nickel–cobalt) are hard to magnetise but hold it for long, so they make permanent magnets.

How do we make or destroy a magnet? To make one, stroke a steel bar repeatedly in one direction with one pole of a strong magnet (single touch) or with two opposite poles (double touch). The most effective way is the electrical method: place the bar in a solenoid and pass a direct current. To destroy a magnet, heat it, hammer it, or place it in a coil carrying an alternating current. Keeping bar magnets in pairs with opposite poles together and a soft-iron keeper across the ends prevents slow loss of magnetism.

One last and very exam-friendly idea: superconductors. Below a critical temperature, some materials lose all electrical resistance and, in addition, push magnetic field lines completely out of their interior. This is the Meissner effect, discovered by Walther Meissner and Robert Ochsenfeld in 1933, and it makes a superconductor a perfect diamagnet. Because the magnet is then repelled and floats above it, the effect is the basis of magnetic levitation (maglev) trains.

For centuries electricity and magnetism were thought to be two unrelated subjects. Then, in 1820, the Danish physicist Hans Christian Oersted was giving a lecture in Copenhagen. A compass lay near a wire. When he switched the current on, the compass needle suddenly deflected; when he switched it off, the needle swung back. With one small observation he proved that an electric current produces a magnetic field around it. Electromagnetism was born, and soon after, Ampère worked out its mathematics.

What does the field of a straight current-carrying wire look like? It forms concentric circles around the wire, in a plane perpendicular to it. The direction is given by the right-hand thumb rule (also called Maxwell's right-hand grip rule): *imagine holding the wire in your right hand with the thumb pointing along the current; the curled fingers show the direction of the magnetic field lines.* Check it with a vertical wire carrying current upwards: the thumb points up, and viewed from above, the fingers curl anticlockwise. Reverse the current and the circles reverse to clockwise.

Bend the wire into a circular loop and the circular field lines near the wire become larger and larger circles farther away, until at the centre of the loop they look like a straight line perpendicular to the plane of the loop. All the field lines inside the loop point in the same direction, so a coil of N turns gives a field N times as strong. Two long parallel wires also affect each other: currents in the same direction attract, currents in opposite directions repel. This force between parallel currents is the basis for the definition of the ampere.

One loop of wire gives a weak field. Wind many loops side by side on a cardboard tube, like a spring, and you get a solenoid: a long coil of insulated copper wire. Each turn adds to the field of the others, so a current through a solenoid produces a field that looks exactly like that of a bar magnet: it has a North end and a South end. Inside a long solenoid the field is strong and nearly uniform (parallel, equally spaced lines), given by B = μ₀ n I, where n is the number of turns per unit length and I the current.

Put a rod of soft iron inside the solenoid and the iron itself becomes a strong magnet as long as the current flows. This is an electromagnet, first made by William Sturgeon in 1824 and greatly improved by Joseph Henry. Its great advantage over a permanent magnet is control: switch the current off and the magnetism disappears; change the current and you change the strength; reverse the current and you reverse the poles. That is why cranes lift heavy scrap iron with electromagnets and drop it by cutting the current, why scrapyards separate magnetic material from junk, and why electric bells, telegraphs, relays, loudspeakers and MRI machines all depend on them.

Now the reverse of Oersted's discovery. If a current can create a magnetic field, a current-carrying wire placed in another magnetic field must feel a force, because two magnetic fields interact. The force is largest when the wire is at right angles to the field (F = B I L sinθ, so F = B I L at 90°) and zero when the wire runs parallel to it. Its direction is given by Fleming's left-hand rule: *stretch the thumb, forefinger and middle finger of your left hand at right angles to one another. If the fore-finger points along the magnetic Field (N to S) and the middle finger along the Current, then the thumb points in the direction of the force (Thrust/Motion) on the conductor.*

An electric motor puts this force to work. A rectangular coil (the armature) is placed between the poles of a magnet. By the left-hand rule, the two long sides carry currents in opposite directions, so one is pushed up and the other down, which spins the coil. After half a turn the coil would be pushed back, so a split-ring commutator reverses the current at exactly that moment, keeping the turning in one direction. Carbon brushes press on the commutator and bring the current in from the battery. The motor converts electrical energy into mechanical energy. Speed and power rise with more current, more turns, a stronger magnet and a larger coil.

The same force also lies behind meters and speakers. In a galvanometer, a coil with a pointer turns in a magnetic field by an amount proportional to the current. Add a low-resistance shunt in parallel and you have an ammeter (connected in series in the circuit); add a high resistance in series and you have a voltmeter (connected in parallel across the part measured). In a loudspeaker, a varying current in a coil in a magnetic field moves a paper cone to and fro and makes sound; a microphone is the reverse, turning sound vibrations into a varying current.

Oersted showed that electricity makes magnetism. Michael Faraday asked the opposite question: can magnetism make electricity? He wound a coil, connected it to a sensitive meter (galvanometer) and pushed a bar magnet into it. The needle jumped! Pull the magnet out and it jumped the other way; hold the magnet still inside and the needle stayed at zero. In 1831 Faraday had discovered electromagnetic induction: *whenever the magnetic flux linked with a coil changes, an emf (and so a current, if the circuit is closed) is induced in it.* The American scientist Joseph Henry found the same effect independently around the same time.

Behind all this is magnetic flux (Φ), the amount of magnetic field passing through a surface: Φ = B A cosθ, with unit weber (Wb). Flux can be changed in three ways: by moving the magnet or the coil, by changing the area or the angle of the coil in the field, or by changing the current in a nearby coil. Faraday's laws: (1) an emf is induced whenever the flux through a circuit changes; (2) the size of the emf equals the rate of change of flux (e = −N ΔΦ/Δt for N turns). A faster change, more turns, or a stronger field gives a bigger emf. A rod of length L moving with speed v at right angles to a field B has an induced emf e = B L v.

In which direction does the induced current flow? Lenz's law (Heinrich Lenz, 1834) answers: *the induced current flows in a direction such that it opposes the change in magnetic flux that produced it.* Push the North pole of a magnet towards a coil: the face of the coil nearest the magnet becomes a North pole too, and pushes it back. Pull the magnet away: that face becomes a South pole and tries to hold it back. Nature is stubborn and always resists the change. This is not a mere curiosity; it is the law of conservation of energy at work, because you must do work against this opposition, and that work is what turns into electrical energy. The minus sign in Faraday's formula is Lenz's law.

Faraday tells you HOW MUCH emf is induced (rate of change of flux). Lenz tells you the DIRECTION of the induced current (opposes the change). Fleming's right-hand rule is the quick hand-trick for the direction when a conductor moves in a field. All three describe one phenomenon.

Fleming's right-hand rule (generator rule): *stretch the thumb, forefinger and middle finger of your right hand at right angles to each other. If the forefinger points along the Field and the thumb along the motion of the conductor, then the middle finger gives the direction of the induced Current.* The fingers are the same as in the left-hand rule; but here the conductor is moved by us (cause = motion) and the current is produced (effect). Use the left hand for motors and the right hand for generators.

An AC generator (alternator, dynamo) uses induction on a big scale. A rectangular coil (the armature) is rotated in a strong magnetic field by a turbine driven by falling water, steam, wind or a bicycle wheel. As the coil turns, the flux through it keeps changing, so an emf is induced. The ends of the coil are joined to two slip rings, which rub against carbon brushes, so the output is alternating: it reverses direction every half rotation. The emf is zero when the plane of the coil is perpendicular to the field (flux is maximum but not changing), and maximum when the plane of the coil is parallel to the field (flux is zero but changing fastest). Replace the slip rings by a split-ring commutator and the output is direct (DC) but pulsating.

Your phone charger takes the 230 V of the wall socket and gives your phone only about 5 V. A power station sends electricity across hundreds of kilometres at several lakh volts. The device that makes both possible is the transformer, which raises or lowers an alternating voltage without changing its frequency. It has no moving parts. It simply uses mutual induction: when the current in one coil changes, the changing flux it creates links with a neighbouring coil and induces an emf in it.

Why do we bother? Because electricity is lost as heat in the transmission wires. Power lost is I²R, where R is the resistance of the long line. For the same power P = V I, if the voltage is raised 100 times, the current falls to one-hundredth, and the heat loss falls to one ten-thousandth. That is why power stations first step up the voltage to very high values, the power is carried over the grid at high voltage (India's highest AC transmission lines are 765 kV), and then at city sub-stations the voltage is stepped down in stages, finally to about 230 V for homes. A transformer works only on AC, which is the main reason AC was chosen for power supply over DC.

Real transformers are not perfect. Their small losses are of four kinds: copper loss (heating of the windings, I²R), eddy-current loss (currents induced in the iron core itself, reduced by using thin insulated laminations), hysteresis loss (energy spent in repeatedly magnetising and demagnetising the core, reduced by soft iron) and flux leakage. Even so, large transformers have efficiencies above 95 per cent, and they are cooled by circulating oil.