Faraday's induction experiment: how does a magnet make a current in a coil?

The phone charger in your socket, the electricity from a wind turbine, the lamp lit by a bicycle dynamo... All of them rest on the same physical effect: a changing magnetic field drives an electric current in a conductor. This is called electromagnetic induction. The first person to show it systematically was Michael Faraday, working in the laboratory of the Royal Institution in London in the autumn of 1831. In this article we look at Faraday’s experiments, at their really surprising result (why a magnet that is standing still produces no current at all), at the expression we now call Faraday’s law, $\varepsilon = -N\,\dfrac{d\Phi}{dt}$, and at the meaning of its minus sign, Lenz’s law. At the end we see how induction works in generators and transformers.

From Ørsted’s compass to Faraday’s question

In 1820 the Danish physicist Hans Christian Ørsted showed that a wire carrying a current deflects a nearby compass needle. In other words, an electric current produces a magnetic effect. The discovery soon led to the first electromagnets.

The natural question was the reverse: can magnetism produce an electric current? Many researchers put a strong magnet next to a wire and looked for a current, and found none. Faraday himself tried several times during the 1820s without success. The trouble was that everyone expected a stationary magnet to produce a steady current. Nature’s answer was different.

29 August 1831: the iron ring

Faraday made a ring of soft iron about 15 cm across. On one side he wound a coil of insulated copper wire (A), and on the other side a second coil (B). The two coils were not connected electrically; only the iron lay between them. He joined the ends of coil B to a long wire that ran over a magnetic needle: the needle would show whether a current was flowing in the wire. The arrangement was a simple form of the instrument that detects current, the galvanometer.

The moment he connected coil A to a battery, the needle moved clearly, swung a few times and came back to where it started. Current kept flowing in coil A, yet there was no current in B. The moment he broke the battery connection, the needle moved again, this time the other way.

The conclusion was clear: the current in B appeared while the current in coil A (and the magnetic field it set up in the iron) was changing. A steady current meant a steady magnetic field, and a steady field produced nothing in B. This ring is the first example of the transformer found today in many electrical devices.

17 October 1831: the magnet and the coil

A few weeks later Faraday obtained the same result without a battery, using only a magnet. He wound many metres of insulated copper wire on a reel, connected the ends of the wire to a galvanometer and quickly pushed a cylindrical bar magnet into the reel. The needle swung one way. When he pulled the magnet back out, the needle swung the other way. When the magnet stayed still inside the reel, the needle stayed at zero.

The observations from this experiment carry all the basic features of induction:

1. A current appears only during the motion. While the magnet rests inside or outside the coil, however strong it is, there is no current.
2. The direction depends on the direction of motion. Pushing and pulling swing the needle in opposite directions. Turning the magnet round and pushing it in south pole first also reverses the swing.
3. Faster motion gives a larger swing. Pushing the same magnet in faster swings the needle further.
4. More turns and a stronger magnet increase the effect. A coil with more turns, or a stronger magnet, gives a larger swing.

One important point: pushing the coil towards the magnet gives the same result. What matters is not which one moves, but that the magnetic field through the coil changes.

What is magnetic flux?

Faraday explained these observations with a picture he called “lines of force”: the space around a magnet is filled with invisible lines that leave its north pole and enter its south pole. When the amount of these lines passing through a loop of wire changes, a current appears in the loop. Today we call this “amount of field passing through a loop” the magnetic flux and write it with the letter $\Phi$ (phi).

In the simple case where the field crosses the surface at right angles and is uniform across it, the flux is the product of the magnetic field and the area:

Here $B$ is the magnetic field (unit: tesla, T) and $A$ is the cross-sectional area of the loop (m²). The unit of flux is the weber: 1 Wb = 1 T·m². If the field crosses the surface at an angle, only its perpendicular component counts: $\Phi = B \cdot A \cdot \cos\theta$.

Flux can change in three ways: the field strength changes (a magnet comes closer or moves away, the current in an electromagnet is switched on or off), the area of the loop changes, or the angle changes (the loop or the magnet turns). All three produce a voltage.

Faraday’s law: ε = −N·dΦ/dt

The quantitative law of induction is written as:

• $\varepsilon$ (epsilon): the induced electromotive force in the coil, that is, a voltage (volts).
• $N$: the number of turns. Every turn sees the same change of flux, so the voltages of the turns add up.
• $\dfrac{d\Phi}{dt}$: the rate of change of the flux (webers per second). What matters is not the flux itself but how fast it changes.

All the observations are in this one line. When the magnet is still, the flux is constant, $d\Phi/dt = 0$ and the voltage is zero. A fast motion changes the flux in a short time, so $d\Phi/dt$ is large. Doubling the number of turns doubles the voltage. If the coil is part of a closed circuit, this voltage drives a current set by the resistance of the circuit.

Faraday did not write the law in this form; he described his results in words and with lines of force. The mathematical form of the law took shape in the 1840s through the work of Franz Neumann and later James Clerk Maxwell. In the same years Joseph Henry in America also found induction independently of Faraday, but he published his results after Faraday.

Lenz’s law: what does the minus sign say?

In 1834 the Russian-German physicist Heinrich Lenz summed up the direction of the induced current in a rule: the induced current flows in the direction that opposes the change of flux that produces it. The minus sign in Faraday’s law expresses this rule.

Think of an example. You push the north pole of a magnet towards a coil. The flux through the coil, pointing from the magnet into the coil, increases. The current set up in the coil produces a field in the opposite direction, opposing this increase: the end of the coil facing the magnet behaves like a north pole and pushes back on the approaching north pole. When you pull the magnet away, the flux decreases; the current reverses, the end of the coil behaves like a south pole and pulls back on the departing magnet.

This rule is really the conservation of energy. If the induced current helped the change, one push on the magnet would make it speed up by itself, and you would get unlimited electrical energy for nothing. In reality you have to apply a force to push the magnet; the work you do becomes electrical energy in the circuit. This is also why the pedals of a bicycle feel a little heavier while the dynamo is lighting the lamp.

Worked example: pushing the magnet into the coil

Let us calculate with the values used in the figure above. The coil has 400 turns and a cross-sectional area of 4 cm². The magnet is a 12 × 12 × 60 mm bar with a remanent magnetisation of 0.4 T. In the figure’s model, when the magnet sits right in the middle of the coil the average field in the coil is about 0.38 T, and the flux through one turn is:

When the magnet is far away, the flux is almost zero. Suppose we push the magnet from far away to the middle of the coil in 0.2 seconds. The average induced voltage is:

If we make the same motion in 0.1 seconds, the change of flux stays the same but the time is halved: the voltage is about 0.6 V. When the magnet stops in the middle, the flux is still 0.15 mWb, but because it no longer changes, the voltage is zero. This difference between the size of the flux and the size of the voltage is the key to understanding induction.

(The 0.38 T comes from the figure’s simple model: the field on the magnet’s axis is taken to be the same across the whole cross-section of every turn. This model overstates the flux. In reality the field is this strong only inside the magnet, and outside it the field turns back the other way; at these sizes the real flux and voltage come out at roughly a third of these values, though the order of magnitude is the same.)

A steady current: the copper disc and the first generator

Pushing a magnet back and forth only gives short pulses of current. For a steady current the motion must be continuous too. On 28 October 1831 Faraday turned a copper disc between the poles of a strong horseshoe magnet and drew a steady current from wires touching the centre and the rim of the disc. This arrangement, the Faraday disc, is counted as the first electric generator.

Today’s generators work on the same principle, but usually with coils turning in a magnetic field, or magnets turning inside coils. The flux through a coil turning in a uniform field changes as $\Phi = B\,A\cos(\omega t)$, so the induced voltage rises and falls like a sine wave:

This is where the alternating current in a socket comes from (50 Hz in Türkiye and Europe): the rotation of the power station’s generator reverses the direction of the voltage 50 times a second each way. What water turns in a dam, wind turns in a wind turbine and steam turns in a thermal power station is always a generator.

An electric motor is a generator run the other way: a current is fed to a coil and the magnetic force turns the coil. But because the flux through the turning coil also changes, induction happens inside the motor too: a voltage appears in the motor’s coil that opposes the voltage applied to it. This is another face of Lenz’s law.

The transformer: where is Faraday’s ring today?

Faraday’s iron ring is the very same thing as today’s transformer. Two coils are wound on a shared iron core. An alternating voltage is applied to the first coil; the flux in the core changes all the time and induces a voltage in the second coil. In an ideal transformer the voltages of the two coils are in proportion to their numbers of turns:

For example, to get about 12 V from the 230 V mains, the second coil must have about one twentieth of the turns of the first. At power stations, the voltage is stepped up by transformers to hundreds of thousands of volts to reduce losses on long lines, and stepped down again near towns and cities.

Faraday’s ring also explains why a transformer does not work with direct current: if the current in the first coil is steady, the flux is steady and no voltage appears in the second coil. Faraday’s needle, too, moved only at the moments he connected and disconnected the battery.

Induction has other everyday examples as well. On an induction hob, currents induced in the base of the pan heat it. In a wireless charger, two flat coils work like a small transformer with air between them. The magnetic pickups of an electric guitar turn the changing flux caused by the vibrating steel strings into a voltage.

Common misconceptions

• “A strong magnet produces a current in a coil.” No; a stationary magnet produces no current, however strong it is. What is needed is a change of flux.
• “The bigger the flux, the bigger the voltage.” The voltage depends not on the size of the flux but on how fast it changes. With the magnet resting in the middle of the coil the flux is at its largest and the voltage is zero.
• “The minus sign means the voltage is negative.” The minus sign tells the direction: the induced current opposes the change.
• “Induction means free energy.” Because of Lenz’s law, moving the magnet takes work; the electrical energy you get comes from that work.

A school experiment: coil, magnet and a sensitive meter

You can easily repeat this experiment in a school laboratory. You need a coil of a few hundred turns (the ready-made coils in school labs are fine), a bar magnet, and a centre-zero galvanometer or a meter that can measure millivolts. Connect the ends of the coil to the meter, push and pull the magnet at different speeds, hold it still inside, then turn it round and repeat. The voltages in this experiment are in the millivolt range; no battery or mains electricity is needed.

Strong neodymium magnets, however, can pinch fingers, can shatter when they snap together and can damage electronic devices and cards. Handle them with care and store them apart.

In summary

• In 1831 Faraday showed that a changing magnetic flux produces a voltage and a current in a coil: first with the iron ring, then with a magnet and a coil.
• When the magnet stops, the flux does not change and there is no current; pushing and pulling give currents in opposite directions.
• Faraday’s law: $\varepsilon = -N\,d\Phi/dt$. The voltage is proportional to the number of turns and to the rate of change of the flux.
• The minus sign is Lenz’s law: the induced current opposes the change that produces it. This follows from the conservation of energy.
• Generators keep the flux changing with turning coils and produce alternating current; transformers step voltage up or down through a changing flux.

You can read how electricity is shared in circuits in our article on series and parallel circuits, and browse our other physics articles and science topics.