The motor effect, induction and Lenz's law

The force on a current-carrying conductor

A wire carrying a current in a magnetic field feels a force. The size depends on the field strength, the current, the length of wire in the field, and the angle between the current and the field - maximum when they are perpendicular and zero when they are parallel.

That last part is where a surprising number of marks go. A wire lying along the field lines feels no force at all, no matter how large the current is, because there is no component of the current perpendicular to the field. If a question gives you an angle, it is giving it to you for a reason.

The direction is perpendicular to both the current and the field, which is why every hand rule in this topic has three mutually perpendicular directions in it. Pick one rule and use only that one. Students who switch between conventions mid-paper are the ones who end up with a force pointing into the page when it should point out.

Why a coil turns, and why it stops turning

Put a rectangular coil in a field and the two sides carrying current across the field feel forces in opposite directions. That pair of opposite forces produces a torque, and the coil rotates. The sides running parallel to the field contribute nothing, which is again the angle rule doing the work.

The torque is largest when the plane of the coil is parallel to the field and zero when the coil has turned so its plane is perpendicular to it. At that position the forces are still there and still opposite, but they now act along the same line, so there is nothing to turn the coil - it only carries on because of its own momentum.

That zero-torque position is the whole reason a commutator exists. It reverses the current at exactly that moment, so that as the coil swings past, the forces reverse too and keep pushing it the same way round. Without it the coil would oscillate and settle.

Induction: it is the change that matters

An emf is induced when the magnetic flux through a circuit changes. Not when there is flux - when it changes. A coil sitting still in an enormous field has an enormous flux through it and no induced emf whatsoever.

The size of the induced emf depends on how fast the flux is changing and how many turns the coil has. So there are three ways to induce one: move the magnet, move the coil, or change the field strength. And there is a fourth that catches people out - change the area of the circuit, or change its orientation, since flux depends on the component of field perpendicular to the loop.

When a question describes a magnet at rest inside a coil and asks for the induced emf, the answer is zero, and the reason is that nothing is changing. Say the reason.

Lenz's law is conservation of energy

The induced current flows in whatever direction opposes the change that produced it. Push a north pole towards a coil and the coil's near face becomes a north pole, pushing back. Pull it away and the near face becomes a south pole, pulling it back.

Learn it as energy rather than as a rule about directions, because then you never have to remember which way round it goes. If the induced current helped the change instead of opposing it, the magnet would accelerate on its own, generating more current, which would accelerate it further - free energy out of nothing. The opposition is the reason that does not happen, and it is why you have to do work to generate electricity.

This is the single best sentence to have ready for an extended response in this module: the induced effect opposes the change because the energy has to come from somewhere, and it comes from whoever is doing the moving.

Back emf, and why a motor draws most current at the start

A motor is also a generator. The moment its coil starts turning, the flux through it is changing, so an emf is induced in it - and by Lenz's law that emf opposes the supply driving it. That is back emf.

It explains behaviour you can observe. At the instant of switching on, the coil is not yet turning, there is no back emf, and the current is at its largest - which is why lights dim when a large motor starts. As the motor speeds up the back emf grows and the current falls. Load the motor so it slows down, and the back emf falls, the current rises, and the motor heats up. A motor stalled under load can draw enough current to burn out, and now you can say exactly why.

Eddy currents are the same idea in a solid conductor: a changing flux induces circulating currents, those currents oppose the motion, and the energy goes to heat. That is a brake when you want one and a loss when you do not, which is why transformer cores are laminated.

Where it usually goes wrong

Almost every lost mark in this module is one of these five.

• Answering a direction question without stating which hand rule you used and what each finger represented.
• Forgetting the angle: no force when current is parallel to field, no induced emf when flux is not changing.
• Quoting Lenz's law without saying why it must be that way. The energy argument is usually worth a mark by itself.
• Describing a commutator as the thing that makes the coil turn. The forces make it turn; the commutator keeps it turning the same way.
• Treating back emf as a fault. It is the motor behaving correctly, and it is what limits the current.

What to practise next

Take six direction questions and answer every one of them in the same two sentences: which rule you used with what pointing where, and then the direction. Consistency is what stops the sign errors, not cleverness.

Then write the energy argument for Lenz's law from memory in three sentences. If you can produce that under pressure, the extended response in this module is largely done before you start.

Check yourself

Three questions on what is above. Have a go before you open them - reading an answer you have not tried to give is the version of this that does nothing.