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Induction — the electric motor and the generator

A current in a magnetic field produces motion, and motion in a magnetic field produces current. Every motor in a washing machine and every generator in a power plant rests on this one symmetry. Push a wire with the Lorentz force, look inside the commutator, crank the generator and slide a magnet into a coil — just as Faraday did in 1831.

6.0 V
20 mN·m

How does it work?

Four steps from a wire in a magnet's field to the power plant. The card for the current mode is highlighted.

01 · LORENTZ FORCE

A current in a magnetic field feels a force

The magnet's field acts on every electron flowing in the wire with the Lorentz force. All these tiny forces add up to the electrodynamic force that pushes the whole wire. When the wire is perpendicular to the field lines:

F=B·I·L

B — magnetic flux density [T], I — current [A], L — length of wire in the field [m]. When the wire runs at an angle, the force gets smaller: F = B·I·L·sin α.

Left-hand rule: hold your left hand so the field lines enter your palm and your four fingers point along the current — your outstretched thumb then shows the direction of the force. Reverse the current or the magnet and the force flips; reverse both and it stays the same.

02 · DC MOTOR

Commutator and back EMF

Forces in opposite directions act on the two sides of the loop — together they create a torque that turns the loop (the armature):

M=N·B·I·A·sin θ

θ — angle between the loop's normal and the field lines, A — area of the loop, N — number of turns. After half a turn, sin θ changes sign and the loop would start turning back. The commutator — a ring split into two halves — reverses the current in the loop at exactly that moment, so the torque always points the same way: M = N·B·I·A·|sin θ|.

The spinning loop is itself a generator: a back EMF ε is induced in it, opposing the supply. The current

I=U − εR

drops as the motor speeds up — that's why a motor has a top speed. A stalled motor (ε = 0) draws the largest current, U/R, and quickly heats up.

03 · GENERATOR

A changing flux makes a voltage

Magnetic flux tells you how many field lines pass through the loop. When the loop turns with angular velocity ω:

Φ=B·A·cos ωt

By Faraday's law, a change in flux induces a voltage (EMF):

ε=−N·ΔΦΔt=N·B·A·ω·sin ωt

The amplitude εmax = N·B·A·ω grows with the number of turns, the magnet's strength and the speed. The voltage is largest when the flux is zero, because that's when the flux changes fastest. Slip rings give alternating current, while the commutator swaps the loop's ends every half turn and gives a pulsating current in one direction.

04 · FARADAY AND LENZ

Magnet, coil and nature's stubbornness

A voltage appears only when the flux changes — a magnet resting motionless in a coil gives nothing. The faster the motion and the more turns, the bigger the galvanometer's swing:

ε=−N·ΔΦΔt

Lenz's law (it's behind the minus sign in the formula): the induced current flows so that its field opposes the change that caused it. Bring the N pole closer, and the coil turns its own N pole to face it and pushes the magnet away. Pull it away, and the coil shows an S pole and holds it back. That's why producing current always takes work.

Model simplifications. The field between the poles is uniform, the loop is a single coil with N turns, we ignore the windings' inductance and the brushes' resistance, and the bar magnet in Faraday mode is treated as a pair of magnetic poles. The motor in the animation turns 25 times slower than in reality (the readings show the real speed), and the generator's crank turns the loop without gearing. The numbers are approximate, but the relationships are real.

Did you know…?

Three facts about machines that turn current into motion and motion into current.

  1. The power in your wall socket is 50 turns per second. Large generators in coal and gas power plants usually have one pair of poles and spin exactly 3,000 times a minute. One turn is one full cycle of the voltage — hence the 50 Hz of the Polish grid.
  2. Nearly half the world's electricity drives motors. According to the International Energy Agency, electric motors in pumps, fans, compressors and machines use about 45% of all electricity worldwide.
  3. A motor can become a generator. When a tram or an electric car brakes, it switches its motors into generator mode: the wheels turn the rotors, and the recovered energy goes back to the grid or the battery. The resistance that slows the vehicle is Lenz's law in practice.

Challenges

The page detects each challenge on its own. The number tells you which mode to look in.

  1. Push the wire left and rightMODE 1 Turn on the current, then reverse the current or the magnet. The swing must exceed 10° each way. Done! The force flips along with the current or the field — exactly as the left-hand rule says.
  2. Stall the motor by overloading itMODE 2 Get the motor up to speed (at least 3 V), then increase the load until the rotor stops. Done! With no rotation there's no back EMF, so the current jumps to U/R — that's how stalled motors overheat.
  3. Make a 12 V amplitude by cranking the generatorMODE 3 Crank faster, or raise the drive speed, the number of turns or the magnet's strength. Done! εmax = N·B·A·ω — each of the four factors works the same way.
  4. Swing the galvanometer needle left and rightMODE 4 Push the magnet in and pull it out fast enough for the needle to pass half the scale each way. Done! Moving the magnet closer and moving it away give currents in opposite directions.
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From history

In 70 years from a compass needle to motors driving factories.

  1. 1820

    Hans Christian Ørsted

    Notices that a wire carrying a current deflects a compass needle. It's the first proof that electricity and magnetism are linked.

  2. 1821

    Michael Faraday

    Builds an “electromagnetic rotator”: a current-carrying wire circles around a magnet standing in mercury. It's the first ancestor of the electric motor.

  3. 1831

    Faraday discovers induction

    On August 29, 1831, he notices a current induced in a coil when a second coil is switched on and off. Soon he builds the first generator — a copper disc spinning between the poles of a magnet.

  4. 1832–1834

    Pixii, Lenz and Jacobi

    Hippolyte Pixii builds a hand-cranked generator and adds a commutator to it. Heinrich Lenz formulates the rule for the direction of induced current, and Moritz Jacobi in Königsberg builds the first practical motor with a rotating armature.

  5. 1888

    Nikola Tesla

    Patents the AC induction motor with a rotating magnetic field. Its descendants work today in pumps, drills and trains.