Lenz's law

Push a magnet into a coil connected in a complete circuit and the needle of a meter flicks one way; pull it out and it flicks the other way. Lenz’s law tells you which way, and the answer comes from one simple rule. It also identifies the mechanical work that supplies electrical energy in this generator arrangement.

Lenz’s law

The direction of the induced e.m.f. is such that its effect opposes the change producing it.

For a magnet and a coil in a complete circuit, the induced current turns the coil into an electromagnet. The coil’s end nearest the magnet becomes a pole that pushes or pulls against the magnet’s motion:

• if the magnet is moving towards the coil, the near end becomes the same pole, so it repels the magnet;
• if the magnet is moving away from the coil, the near end becomes the opposite pole, so it attracts the magnet.

The coil opposes the change, not the magnet itself. When the magnet moves away, the coil attracts it, trying to keep the field in the coil from falling. Once the magnet is held still and brief transients have settled, the linked field is unchanged: no current is driven by this motion and no opposing coil pole remains.

Worked example 1

A north pole approaching

Problem

The north pole of a bar magnet is pushed towards one end of a coil connected in a complete circuit. What pole is induced at that end of the coil? Explain using Lenz’s law.

Show full solution

1. Name the change

   Method

   The north pole is moving towards the coil.

   Reason

   Lenz’s law says the induced effect opposes this change.

   Working

   Answer

   The change to oppose is the approach of a north pole.

2. Choose the pole that opposes it

   Method

   The coil must repel the magnet, so its near end becomes a north pole.

   Reason

   Like poles repel, and repulsion pushes back against the approaching magnet.

   Working

   Answer

   Near end of the coil: north.

Quick check

A south pole at the near end would attract the magnet and help it in, which would break Lenz’s law.

Check your understanding 1

The south pole of a bar magnet is pushed towards a coil in a complete circuit. What pole is induced at the near end of the coil? Explain.

Effect that opposes the approach

Repel the approaching south pole.CorrectIncorrectAttract the approaching south pole.CorrectIncorrect

Near end of the coil

SouthCorrectIncorrectNorthCorrectIncorrect

Check answer

Show answer

A south pole. The coil must oppose the approach, so it repels the magnet, and like poles repel. A north pole at that end would attract the magnet and help the change.

The direction of the induced current

Once you know the pole at the end of the coil, you can find the direction of the current using the rule for a solenoid. Look at that end of the coil:

• if it is a north pole, the current flows anticlockwise round it;
• if it is a south pole, the current flows clockwise round it.

So when the magnet changes from moving in to moving out, the pole at the near end swaps, and the induced current reverses.

Check your understanding 2

A north pole is pulled away from the end of a coil in a complete circuit. Looking at that end from the magnet’s side, does the induced current flow clockwise or anticlockwise? What happens when the magnet is held still?

Near pole during north-pole withdrawal

NorthCorrectIncorrectSouthCorrectIncorrect

Conventional current viewed from the magnet’s side

ClockwiseCorrectIncorrectAnticlockwiseCorrectIncorrect

Current after holding the magnet still and allowing transients to settle

AUnit: A

Check answer

Show answer

Clockwise. The coil must attract the departing north pole to oppose its motion, so the near end becomes south. Seen from that end, a south pole has clockwise current. After the magnet is held still and brief transients settle, the induced current is zero because the linked field is no longer changing.

Exam-style question 1

A south pole moving away

3 marks

Examination question

The south pole of a magnet is pulled away from the end of a coil connected in a complete circuit. State the pole induced at that end of the coil, explain your answer using Lenz’s law, and compare the direction of the induced current with the case when the south pole was pushed in. [3 marks]

Oppose the movement away

State all three parts: induced pole, opposition reason and comparison with the approach current. Work on paper or here, then compare the complete reasoning with the model below. You need not transcribe your paper work.

Optional note from your working or comparison

Show solution step by step

1. State the pole

   1 mark

   Method

   The near end of the coil becomes a north pole.

   Reason

   The answer must name the pole before explaining it.

   Working

   Answer

   Near end: north pole.

2. Explain with Lenz's law

   1 mark

   Method

   A north pole attracts the departing south pole.

   Reason

   The induced effect must oppose the change, which here is the magnet moving away.

   Working

   Answer

   Unlike poles attract, opposing the movement away.

3. Compare the current

   1 mark

   Working

   Answer

   When the south pole was pushed in, the near end was a south pole. The pole has swapped, so the induced current flows in the opposite direction.

Self-mark with the mark scheme

Tick each mark point that your answer includes.

Mark the pole, the reason and the current comparison separately.

Mark points

1. 1 mark: States that the near end of the coil is a north pole.
2. 1 mark: Explains that the attraction opposes the magnet moving away.
3. 1 mark: States that the induced current is reversed compared with pushing the magnet in.

Calculate your mark

Lenz’s law and energy

For the same motion through an air-cored coil in a complete conducting circuit, the induced magnetic effect resists the motion. You must do extra work against it, whether moving in or out. That work supplies the electrical energy transferred to the circuit; holding a magnet still does not supply a continuous electrical output.

Imagine Lenz’s law were the other way round. An approaching magnet would be pulled in, which would speed it up and induce an even larger current, which would pull harder still. You would get electrical energy and kinetic energy from nothing. Energy cannot be created, so the induced effect must oppose the change.

Check your understanding 3

A magnet follows the same entry path at the same speed through an air-cored coil, first in a complete resistive circuit and then with that circuit broken. In which case is the magnet harder to push? Explain where the energy goes.

Same magnet, air-cored coil and motion: harder to push

Broken circuitCorrectIncorrectComplete circuitCorrectIncorrectSame push in either circuitCorrectIncorrect

Extra work in the complete resistive circuit

Mechanical work supplies only magnetic storage.CorrectIncorrectMechanical work supplies electrical heating.CorrectIncorrectThe magnet’s energy store supplies electrical heating.CorrectIncorrect

Check answer

Show answer

The complete circuit is harder to push through. Mechanical work supplies electrical energy, which heats its resistance.

Check your understanding 4 Explain the extra work

Explain why completing the circuit changes the force on the moving magnet and where the extra work goes. Include what still happens when the circuit is broken.

Induced current, opposing force and energy transfer

Show answer

It is harder to push when the circuit is complete. Then a current flows, and its magnetic effect repels the magnet, so you must do work against it. That work is changed into electrical energy, which heats the coil and the rest of the circuit. With the circuit broken, an e.m.f. can still be induced but no sustained current produces this opposing magnetic effect. With the broken circuit, mechanical friction can still require work; the extra magnetic resistance from induced current is absent.

Check your understanding 5 Change the viewing end

A south pole is pulled away from the left end of an air-cored coil in a complete circuit. On paper, label both induced coil poles and show conventional current as viewed from the left, then from the right. Explain why opposite-looking current descriptions do not imply two currents. Compare your full construction and explanation below; a note is optional.

Optional note from your construction or comparison

Show answer

To oppose withdrawal, the left face is north and attracts the departing south pole; the right face is south. Current is anticlockwise when viewed from the left and clockwise when viewed from the right. It is one circulating current seen from opposite directions. Check both pole labels, both viewing arrows and the connection between the resisting effect and the chosen pole. The current reverses if motion changes to approach with the same south pole, regardless of which viewing convention you use.

Common mistakes

• Saying the coil always repels the magnet. It repels an approaching magnet but attracts a departing one.
• Saying the induced effect opposes the magnet’s field. It opposes the change.
• Forgetting that the induced current reverses when the motion reverses.
• Saying the coil creates energy. The electrical energy comes from the work done in moving the magnet.