Motors and generators

A wire 5 cm long carrying 20 A across a 1.5 T field is pushed with a force of 1.5 N; spin that idea into a loop and you have a motor.

A magnetic field pushes on a current

Unit 4 showed that a current makes a magnetic field. The reverse is also true in a sense: a magnetic field pushes on a current. The force on a straight wire of length l carrying current I across a uniform field B is F = I l B sin θ, where θ is the angle between the wire and the field. The force is largest when the wire crosses the field at right angles and zero when the wire runs along it. Its direction is at right angles to both the wire and the field, and right hand rule 1 in OpenStax gives which way.

OpenStax works out an example with a strong field: B = 1.50 T, a 5.00 cm length of wire and a current of 20.0 A. With sin 90° = 1, F = 20.0 × 0.0500 × 1.50 = 1.50 N, about the weight of a 150 g apple. That is a noticeable push on a short piece of wire. It also shows where the tesla comes from: 1 T is the field in which 1 A in 1 m of wire feels 1 N.

From a push to a spin: the electric motor

Put a rectangular loop of wire between the poles of a magnet and pass a current round it. On one side the current flows one way and on the opposite side the other way, so the two sides are pushed in opposite directions. The loop twists. If nothing changed, it would rock to a stop facing the field, so a motor reverses the current every half turn. In a direct current motor, a split-ring commutator and brushes do this, so the loop keeps turning the same way as long as the current flows. The twist grows with the number of turns: OpenStax works out that a 100-turn square coil 10.0 cm on a side, carrying 15.0 A in a 2.00 T field, feels a maximum torque of 30.0 N·m, enough to be useful in a motor. OpenStax's table of efficiencies gives electric motors about 98 percent, far above engines that burn fuel.

Turning motion back into electricity

If a current in a field can make motion, can motion in a field make a current? Michael Faraday spent years on this question. On 29 August 1831, in his basement laboratory at the Royal Institution in London, he wound two coils of wire on opposite sides of an iron ring. When he connected a battery to one coil, a needle connected to the other coil twitched for a moment, then settled. When he disconnected the battery it twitched the other way. A steady current in the first coil did nothing to the second; only a change did. The Royal Institution, which still keeps the ring, describes it as the first electric transformer.

This is electromagnetic induction: a changing magnetic field through a coil produces a voltage, called an induced emf. Push a bar magnet into a coil and a meter on the coil swings one way; pull it out and it swings the other way; hold it still and the meter reads zero. Move it faster and the reading is bigger. OpenStax states the key quantity as magnetic flux, Φ = B A cos θ, the field times the area of the loop it passes through. Any change in flux induces an emf, whether the field changes, the area changes or the loop turns.

A generator turns this into a machine. A coil spins between magnets, so the angle θ and therefore the flux keep changing, and an alternating voltage appears at its ends. A generator is built almost exactly like a motor: in a motor, electrical energy becomes rotation, and in a generator, rotation becomes electrical energy. Turbines turned by steam, falling water or wind spin the generators that supply most of the electricity in our homes.