DC Motors

Send a current through a loop of wire sitting between two magnets, and the wire suddenly twists and spins. That spinning loop is the heart of a DC motor, the thing that drives fans, drills, electric cars and toy trains. The trick is that a magnetic field pushes on a current, and if you arrange that push cleverly, the loop turns the same way round and round forever.

A push on each side of the coil

A DC motor has a coil, a loop of wire with $n$ turns, that is free to spin between the poles of a magnet. When current flows through it, the magnetic field pushes on the wire.

• The force on each long side is $F = nBIL$, where $B$ is the field strength, $I$ the current and $L$ the length of the side.
• The current runs in opposite directions on the two sides of the coil, so the push on one side is up while the push on the other side is down.
• Two equal forces pushing in opposite directions on either side of the coil make it twist. That twisting effect is called torque.

The red arrows are the forces, equal in size but pointing opposite ways, one up on the left side and one down on the right. That pair of pushes is what twists the coil. The blue piece at the bottom is the split ring commutator with its two brushes, which feed current into the coil.

Keeping it spinning the same way

Here is the problem. The coil twists nicely for the first half turn, but once it passes the upright position the forces would start pushing it back the other way. Left alone it would just rock in place. The fix is a clever switch.

A split ring commutator is a ring cut into two halves that turns with the coil. Every half turn the brushes slide from one half to the other, which reverses the current in the coil. Because the current flips at exactly the right moment, the force on each side always drives the coil the same way around, so it keeps spinning.

Try one: the split ring commutator in a DC motor is replaced with slip rings (continuous rings that never break contact with the brushes). Explain what happens to the coil.

See it for yourself

A motor runs on the magnetic field a current makes. Switch to the electromagnet, change the current, and watch the field it builds. That is the field that pushes against the outside magnets and spins the coil.

How strong is the twist?

The size of the turning effect is the torque, and it depends on four things: the number of turns, the field strength, the current and the area of the coil.

There is no torque formula to memorise for this course. The turning effect simply grows with each of those four, so to build a stronger motor you can add more turns, use a stronger magnet, push more current, or use a bigger coil.

The torque also changes as the coil spins. It is greatest when the plane of the coil is parallel to the field, because the forces then act at the full distance across the coil. It drops to zero when the plane of the coil is perpendicular to the field, where the forces line up along the coil and have nothing to twist against. A real motor uses momentum to carry the coil through that zero point each half turn.

Energy in, motion out

A DC motor is an energy converter. It takes in electrical energy from the supply and turns it into rotational kinetic energy, the energy of the spinning coil and shaft. A little energy is always lost as heat and sound, but the useful job is making something turn.

Lock it in with active recall

Cover the answer and say each one out loud before you flip. Rate yourself honestly — the cards you find hard come back sooner, the ones you know are spaced further out.

See the formulas in action in the Worked Examples tab, then test yourself in Try It.