Lenz's law: direction and energy
Key idea: An induced current produces a magnetic effect opposing the change that caused it. The mechanical work needed against that effect supplies electrical energy, consistent with energy conservation.
Offline pages
Saved on this device only. Connect at least once every 30 days to confirm Premium. Sign-out or a change of account removes saved copies.
Loading guide controls…
Guided lessons · coming soon
Guided lesson
Guided steps
- Predict the current seen from the magnet’s side. Play Approach, select Hold still, then Withdraw; compare the direction readout and the zero current while held.
- Read why weakening outward flux needs an outward induced field.
- Find the current during increasing flux and during steady flux.
- Describe the same current from opposite sides of the coil.
- Follow the magnet’s work into electrical energy and heating.
- Decide what cutting the coil changes while the magnet moves.
- Find the near pole and current for an approaching south pole.
- Explain the current, force and energy for a withdrawing magnet.
On this page
You stopped at:
ContinueFaraday’s law gives the size of an induced e.m.f.; Lenz’s law gives its direction. The rule is short, but it is easy to misread: the induced current opposes the change in flux, not the flux itself. Behind it is the conservation of energy.
Lenz’s law
Lenz’s law: the direction of the induced e.m.f. is such that it tends to oppose the change producing it. In a closed coil, the induced current sets up its own magnetic field, and that field opposes the change in flux linkage.
To find the direction of the induced current in a coil:
- Say which side you are viewing the coil from, and find the direction of the external flux through it.
- Decide whether that flux is increasing or decreasing.
- Choose the direction of the induced field that opposes the change: opposite to the external field if the flux is increasing, the same way if it is decreasing.
- Use the right-hand grip rule: an anticlockwise current gives a field towards you, a clockwise current a field away from you.
Viewed from a north pole approaching a coil, the external flux points into the coil, away from you, and is increasing. The induced field points towards you, so the current is anticlockwise and the near face of the coil is a north pole, repelling the magnet. When the north pole is pulled away, the inward flux decreases; the induced field is inward, the current clockwise and the near face a south pole, attracting the magnet back.
Lenz investigation, viewed from the magnet’s side. North pole faces the coil. The magnet is held still; induced current is zero. Current equals e.m.f. divided by resistance; self-inductance is neglected.
- Current, viewed from magnet
- zero
- Motion
- held still
- Force on 1 m of wire
- 0 mN
- B at compass 1
- 7.02 μT
- Compass 1 from the wire
- 11.4 cm
- B inside the coil
- 0.133 mT
- Induced e.m.f.
- 0 mV
- Current in the meter
- 0 mA
- Magnet speed
- 0.00 m/s
Try this
0 of 1 donePredict each direction, then play Approach, Hold still and Withdraw with the same pole facing the coil. (not done yet)
Approach and withdrawal give opposite currents. Hold gives zero current despite non-zero magnetic flux. Directions are viewed from the magnet’s side; self-inductance is neglected.
You’ve tried every task.
The magnet stays on the near side of a closed coil, and directions are viewed from the magnet’s side. The model uses ε = -d(NΦ)/dt and I = ε/R, and ignores the coil’s self-inductance. On Hold the magnet stops at once, so the current is zero even though flux still links the coil. The meter needle may take a moment to settle; that is not current lingering.
Worked example 1
A weakening field
Problem
A closed loop lies in the plane of the page. A uniform magnetic field through it points out of the page and is decreasing. Find the direction of the induced current, as seen on the page.
Show full solution
The change
Method
State the direction of the flux and how it is changing.Reason
Lenz’s law responds to the change, not to the field itself.Working
Answer
The flux out of the page is decreasing.
Induced field
Method
Choose the field that opposes the decrease.Reason
To resist a fall in outward flux, the loop adds outward flux of its own.Working
Answer
The induced field is out of the page, the same direction as the external field.
Current
Working
Answer
By the right-hand grip rule, a field out of the page comes from an anticlockwise current.
Quick check
The induced field points the same way as the external field here. It does not always oppose the field; it opposes the change.
Guided practice 2
Increasing, then steady
Problem
A magnetic field out of the page is increasing through a closed coil lying in the page. Which way is the induced current, as seen on the page? What is the current once the field stops changing? Treat the circuit as resistive with negligible self-inductance.
Find the current
Hints
Hint 1
oppose, then grip
The outward flux is growing. Choose the opposing induced field, then use the grip rule.
Show full solution
Current
Working
Answer
The induced field is into the page, so the current is clockwise. Once the field is steady, the flux is not changing and there is no current in the stated resistive model.
Spot the mistake 3
“The current is clockwise”
Learner claim
A coil has a north pole on the face nearest a magnet. A student says “the current is clockwise” without saying where the coil is viewed from. Which way is the current seen from the magnet’s side, and from the other side?
Try this before viewing the solution
Show solution step by step
From the north face
Method
Use the grip rule with the field pointing towards you.Reason
Field lines leave a north face, so from that side the coil’s field points at the viewer.Working
Answer
Anticlockwise
From the other side
Working
Answer
Clockwise. The current itself has not changed.
Common mistake
“Clockwise” means nothing until you say which side you are looking from.
Lenz’s law and energy
Lenz’s law follows from the conservation of energy. When a magnet is pushed towards a closed coil, the induced current makes the near face of the coil repel it. You have to do work to keep the magnet moving, and that work becomes the electrical energy in the coil, which ends up heating it.
If the induced current had the opposite direction, the coil would attract the magnet and speed it up. The magnet would then gain kinetic energy and the coil would gain electrical energy, both from nothing. That cannot happen, so the induced current must oppose the change.
If the coil is not a complete circuit, an e.m.f. is still induced, but there is no current and so no opposing force.
Check your understanding 1
A magnet is moving towards a coil. The wire is cut so the coil becomes an open circuit while the magnet keeps moving. What happens to the induced e.m.f. and to the magnetic force from the induced current? Ignore brief switching effects and capacitance.
Show answer
The changing flux still induces an e.m.f. across the open coil. With no complete path, there is no current, so the opposing force from that current disappears. Lenz’s law gives the direction in which the e.m.f. would drive a current if the circuit were closed.
Try it yourself 4
An approaching south pole
Problem
The south pole of a magnet is pushed towards a closed coil along its axis. Viewing the coil from the magnet’s side, find the pole on the near face of the coil and the direction of the induced current.
Find the pole and the current
Hints
Hint 1
field lines
Field lines point towards a south pole, so the external flux through the coil points towards you and is increasing.
Show solution step by step
Flux change
Reason
Field lines run into the approaching south pole, and they get stronger as it gets closer.Working
Answer
The flux towards the viewer is increasing.
Pole and current
Working
Answer
The induced field points away from the viewer, so the current is clockwise. Field lines enter the near face, so it is a south pole, which repels the approaching south pole.
Exam-style question 1
A withdrawing north pole
Examination question
The north pole of a magnet is pulled away from a closed coil along its axis.
(a) State Lenz’s law. [1 mark]
(b) Viewing the coil from the magnet’s side, state the direction of the induced current and whether the coil attracts or repels the magnet. [2 marks]
(c) Explain, in terms of energy, why the coil must act on the magnet in this way. [2 marks]
Write your answer before viewing the mark scheme
Show solution step by step
(a) Lenz's law
1 markReason
Use the standard wording.Working
Answer
The direction of the induced e.m.f. is such that it opposes the change producing it.
(b) Current and force
2 marksMethod
Find the flux change, oppose it, then use the grip rule.Reason
The flux into the coil, away from the viewer, is decreasing, so the induced field also points away from the viewer.Working
Answer
The current is clockwise. The near face is a south pole, which attracts the magnet, opposing its withdrawal.
(c) Energy
2 marksWorking
Answer
Work must be done against the attraction to pull the magnet away, and this work becomes the electrical energy in the coil. If the coil repelled the magnet instead, electrical energy and kinetic energy would both be gained from nothing, which breaks the conservation of energy.
Self-mark with the mark scheme
Tick each mark point that your answer includes.
Tick each point only if your answer states it clearly.
Common mistakes
- Saying the induced field always opposes the external field; it opposes the change in flux.
- Giving “clockwise” or “anticlockwise” without saying where the coil is viewed from.
- Expecting a current to continue after the flux has stopped changing.
- Expecting an opposing force from a coil that is not a complete circuit.
Spotted an error? Report a correction
Syllabus and review details
- GCE A-Level H2 Physics 2027 · 2027
Content Overview, PDF pages 9–10; Subject Content, PDF pages 11–30
Last reviewed: