Lenz's Law and Direction
In 1851, Léon Foucault in Paris swung a copper disc between electromagnet poles and watched it stop in under one second — not from friction, but from eddy currents induced in the copper that opposed the disc's motion. This is Lenz's Law in action. Modern Shinkansen bullet trains in Japan (operating since 1964) decelerate from 320 km/h to zero using this same magnetic braking principle, with zero mechanical contact between braking components.
Practise this lesson
Four printable worksheets that build from the foundations up to exam-style questions — start at whatever level suits you.
A bar magnet approaches a loop of wire with its north pole facing the loop.
- As the north pole approaches, does the magnetic flux through the loop increase or decrease?
- The induced current will create its own magnetic field. Should this induced field point toward the approaching magnet (helping it) or away from it (opposing it)?
- If the induced current helped the magnet instead of opposing it, what would happen to the magnet's speed?
Warm-up — electromagnetic induction occurs when…
Know — Lenz's Law
- The induced current opposes the change in magnetic flux that produced it
- Lenz's Law gives the direction of the induced current
- It is represented by the negative sign in Faraday's Law
Understand — Conservation of Energy
- Lenz's Law ensures energy is conserved in electromagnetic induction
- If the induced current aided the change, energy would be created from nothing
- The work done against the opposing force provides the electrical energy
Can Do — Predict Direction
- Determine the direction of induced current using the right-hand grip rule
- Predict the direction of induced magnetic field for any flux change
- Apply Lenz's Law to real situations
Core Content
Opposition is the key
Push the north pole of a bar magnet toward a coil of wire connected to a galvanometer. As the magnet approaches, you feel resistance — the coil is pushing back. Look at the galvanometer: it deflects, showing a current flowing. That current creates its own magnetic field, and by the right-hand grip rule, this field points away from the approaching north pole — repelling it. Pull the magnet away and the current reverses, now attracting the magnet back. In every case, the induced current acts to oppose whatever change is happening to the flux: this is Lenz's Law.
$\varepsilon = -N \dfrac{\Delta \Phi}{\Delta t}$
The negative sign represents Lenz's Law — it ensures the induced emf opposes the flux change.
How to apply Lenz's Law — four steps:
- Determine the direction of the external magnetic field.
- Determine whether the flux is increasing or decreasing.
- The induced magnetic field must oppose this change: if flux increases, the induced field opposes the external field; if flux decreases, the induced field reinforces the external field.
- Use the right-hand grip rule to find the direction of current that produces this induced field.
A north pole of a magnet is pulled away from a loop. Is the induced current clockwise or anticlockwise when viewed from the magnet's side? Explain your reasoning using Lenz's Law.
Lenz's Law: the induced current opposes the change in flux that caused it (= the negative sign in $\varepsilon = -N\Delta\Phi/\Delta t$). 4-step method: (1) direction of $\vec{B}$; (2) flux increasing or decreasing; (3) induced $\vec{B}$ opposes the change; (4) right-hand grip rule → current direction.
Pause — copy the highlighted Lenz's Law statement and 4-step method into your book before moving on.
Lenz's Law states that the induced current:
Why the opposition is physically necessary
We just saw that Lenz's Law says the induced current opposes flux change. That raises a question: is this opposition just a convenient mnemonic, or is there a deeper physical reason for it? This card answers it → it is demanded by conservation of energy; without opposition, a perpetual motion machine would be possible.
Lenz's Law is not just a convenient rule — it is required by the conservation of energy. Imagine what would happen if the induced current aided the change instead of opposing it:
- A magnet approaches a loop. The induced current creates a field that attracts the magnet, pulling it in faster.
- The magnet speeds up, increasing the flux change, which increases the induced current, which pulls it even faster.
- The magnet would accelerate indefinitely, generating infinite electrical energy from nothing.
This is a perpetual motion machine — impossible. Lenz's Law prevents this by ensuring the induced current opposes the motion. To push the magnet into the loop, you must do work against the repulsive force. This work is converted into the electrical energy of the induced current. Energy is conserved.
In extended response questions, always link Lenz's Law to conservation of energy. Explain that the work done against the opposing magnetic force is the source of the electrical energy.
Lenz's Law is demanded by conservation of energy. If the induced current aided the change, the magnet would accelerate indefinitely, creating infinite energy — impossible. Work done against the opposing magnetic force = electrical energy of the induced current.
Add the highlighted energy argument to your notes before the check below.
If the induced current aided the approaching magnet instead of opposing it, energy would still be conserved.
The work done pushing a magnet into a coil against the magnetic opposition is converted into electrical energy in the circuit.
Lenz's Law is a consequence of conservation of energy.
Use the interactive. A north pole approaches a loop. The induced current creates a field that:
Determine induced current direction in three scenarios
We just saw why Lenz's Law must hold (energy conservation). That raises a question: how do we actually apply the 4-step method to determine which direction a current flows in a specific diagram? This card answers it → work through: direction of B → increasing or decreasing flux → induced B opposes → right-hand grip rule.
A circular loop lies in the plane of the page. A bar magnet with its north pole pointing toward the loop is moved toward the loop from the left.
- (a) Determine the direction of the induced current in the loop when the magnet approaches.
- (b) The magnet is held stationary. What is the induced current?
- (c) The magnet is pulled away. Determine the new direction of the induced current.
- External field: The north pole creates field lines pointing to the right (toward the loop). So B points right through the loop.
- Flux change: As the magnet approaches, flux to the right is increasing.
- Induced field must oppose: It must point to the left (opposing the increase).
- Right-hand grip rule: Thumb points left (induced field). Fingers curl anticlockwise when viewed from the left.
Answer: Anticlockwise (viewed from the left).
No flux change means no induced emf and no induced current. Answer: Zero current.
- External field still points right, but now flux is decreasing.
- Induced field must oppose the decrease: it points right (reinforcing the decreasing field).
- Right-hand grip rule: Thumb points right. Fingers curl clockwise when viewed from the left.
Answer: Clockwise (viewed from the left).
Flux increasing → induced field opposes external field (anticlockwise for N-pole approaching). Flux decreasing → induced field reinforces external field (clockwise for N-pole receding). Stationary magnet → zero flux change → zero current.
Pause — write the highlighted Lenz's Law direction results for the three scenarios into your book before moving on.
A south pole approaches a loop from the left. The induced current viewed from the left is:
Use the interactive above and your knowledge to answer
- With the magnet approaching, observe the induced current direction. Use the right-hand grip rule to verify the induced field repels the approaching magnet.
- What changes when the magnet recedes? Explain why the induced field now attracts the receding magnet.
- A south pole approaches the loop. Predict the current direction and induced field direction before checking.
- Explain how each scenario conserves energy.
Three of these statements about Lenz's Law are correct. Pick the odd one out.
Apply Lenz's Law to a more complex scenario
A coil is dropped from rest through the region between the poles of a strong magnet. As it enters the field, it experiences an upward magnetic force. As it leaves the field on the other side, it also experiences an upward magnetic force.
Explain both effects using Lenz's Law, and link each to conservation of energy.
Flux increasing → induced field opposes external field → induced current creates repulsive force
Flux decreasing → induced field reinforces external field → induced current creates attractive force
Flux unchanged → no induced emf, no induced current
In all cases: work done against the opposing force = electrical energy generated. Energy is always conserved.
A magnet falls through a copper tube. The magnet falls slower than in free fall because:
A fresh five-question set drawn from this lesson's bank — feedback shown immediately. +5 XP per correct · +25 XP all correct
Pick your answer, then rate your confidence — that tells the system what to drill next.
ApplyBand 4(2 marks) 1. A bar magnet with its north pole facing downward is dropped toward a horizontal loop of wire. Determine the direction of the induced current in the loop as the magnet approaches (clockwise or anticlockwise when viewed from above). Show your reasoning using Lenz's Law.
1 mark: correct identification of flux change and opposing field direction · 1 mark: correct current direction with right-hand grip rule applied
AnalyseBand 5(4 marks) 2. Explain why Lenz's Law is a necessary consequence of conservation of energy. In your answer, describe what would happen if the induced current aided rather than opposed the change in flux, and explain what physical principle would be violated.
1 mark: if current aided the change, it would attract the magnet/reinforce motion · 1 mark: this would cause the magnet to accelerate indefinitely · 1 mark: this would create electrical energy from nothing (perpetual motion) · 1 mark: this violates conservation of energy; Lenz's Law ensures work done against opposition equals electrical energy produced
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Multiple choice
MC answers and full explanations are shown inline as you complete each question. Use the retry button to attempt a fresh set drawn from the lesson bank.
Short Answer — Model Answers
Q1 (2 marks): As the north pole approaches from above, the magnetic flux downward through the loop is increasing (flux pointing downward is increasing). By Lenz's Law, the induced magnetic field must oppose this increase, so it points upward (opposing the downward flux). Applying the right-hand grip rule: curl the fingers of the right hand so the thumb points upward (toward the induced field). The fingers curl anticlockwise when viewed from above. Answer: Anticlockwise (viewed from above) (2 marks for correct reasoning and direction).
Q2 (4 marks): If the induced current aided the change: as a north pole approached a loop, the induced current would create a field that attracted the magnet, pulling it in faster (1 mark). This would cause the magnet to accelerate, increasing the rate of flux change, which would increase the induced current, attracting the magnet even more strongly (1 mark). The magnet would accelerate indefinitely, and the loop would continuously generate ever-increasing electrical energy without any external energy input — a perpetual motion machine (1 mark). This violates conservation of energy, which states that energy cannot be created from nothing. Lenz's Law ensures the induced current always opposes the motion, so mechanical work must be done against the opposing force. This work is the source of the electrical energy. Energy is conserved (1 mark).
Five timed questions on Lenz's Law and electromagnetic induction. Beat the boss to bank a tier — gold (perfect + fast), silver (80%+), or bronze (cleared).
⚔ Enter the arenaAt the start you were asked about Foucault's 1851 copper disc experiment in Paris: if the eddy currents had helped the disc's motion instead of opposing it, what would happen to its speed — and why would this violate conservation of energy?
The answer: if the induced current aided the motion, the disc would accelerate. The increasing speed would increase the flux change rate, inducing a larger current, accelerating the disc further — an unstoppable runaway that creates kinetic energy from nothing. Lenz's Law prevents this: induced currents always oppose the change, removing kinetic energy and converting it to electrical energy (then heat). Every time Foucault's disc was pushed, its kinetic energy became eddy-current heat in the copper.
Extend your thinking: A coil is dropped from rest between the poles of a strong magnet. As it enters the field it experiences an upward force; as it leaves the field it also experiences an upward force. Both effects follow from Lenz's Law. Did your Activity 2 answer capture both correctly?