What determines the direction of an induced current, and how does this follow from conservation of energy?
Use Lenz's law to determine the direction of an induced current and explain it in terms of conservation of energy.
How Lenz's law gives the direction of an induced current as the one that opposes the change producing it, and why this is required by conservation of energy.
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What this dot point is asking
You need to use Lenz's law to find the direction of an induced current and explain why it must oppose the change, linking this to conservation of energy.
The statement
This is the source of the minus sign in Faraday's law, : the induced EMF acts against the change in flux.
Applying it to a magnet and a coil
Picture a bar magnet being pushed, north pole first, toward a coil:
- The flux through the coil increases as the magnet approaches.
- By Lenz's law, the induced current opposes this increase, so it must create a magnetic field that pushes the magnet back; the coil's near face becomes a north pole.
- This means you must do work against a repulsion to push the magnet in.
Now pull the same magnet away:
- The flux decreases.
- The induced current now opposes the decrease, so the coil's near face becomes a south pole, attracting the magnet back to try to keep the flux up.
- Again you must do work, this time against an attraction.
Either way, the induced effect resists your motion.
Why: conservation of energy
The electrical energy generated comes from the mechanical work done against the opposing force, not from nowhere.
Eddy currents and braking
Lenz's law explains electromagnetic braking. A conductor moving through a magnetic field has circulating "eddy currents" induced in it. These currents oppose the motion, producing a retarding force that slows the conductor smoothly without contact - used in trains, roller-coasters and gym equipment, and seen when a magnet falls slowly through a copper tube.
How SACE assesses this
SACE Stage 2 Lenz's-law questions usually show a loop entering or leaving a region of field (often drawn out of, or into, the page) and ask for the direction of the induced current, with justification. The dependable three-step method is: state whether the flux is increasing or decreasing, state that the induced current opposes that change (so its own field maintains the original flux), and apply the right-hand grip rule to convert the required internal field into a clockwise or anticlockwise current. Markers award a mark for each of these steps, and a further mark for linking the opposition to conservation of energy. A second common style is the magnet-and-tube or magnet-and-coil scenario, where you explain the retarding force and the conversion of mechanical work into electrical (then heat) energy.
Exam-style practice questions
Practice questions written in the style of SACE Board exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.
SACE 20243 marksA square conductive loop moves out of a region of uniform magnetic field directed out of the plane of the page. Using Lenz's law, determine the direction of the induced current in the loop as it leaves the field, and justify your answer.Show worked answer →
As the loop leaves the field, the outward (out of the page) flux through it is decreasing.
By Lenz's law, the induced current opposes this change, so it acts to maintain the outward flux through the loop.
To create a field out of the page inside the loop, the induced current must flow anticlockwise (right-hand grip rule: thumb out of the page, fingers curl anticlockwise).
Therefore the current is anticlockwise. 1 mark for identifying the flux is decreasing, 1 mark for applying Lenz's law (current opposes the decrease), 1 mark for the anticlockwise direction. The opposition is required by conservation of energy, as the current resists the motion removing the loop.
SACE 20222 marksA strong bar magnet is dropped, north pole downwards, through a vertical copper tube. (a) State whether the magnet falls faster or slower than it would in free fall. (b) Explain your answer using Lenz's law and conservation of energy.Show worked answer →
(a) The magnet falls slower than free fall. (1 mark)
(b) As the magnet falls, the flux through each ring of the tube changes, inducing eddy currents. By Lenz's law these currents oppose the change, so the section ahead of the magnet repels it and the section behind attracts it, producing a retarding force opposite to the motion. By conservation of energy, the gravitational potential energy lost is partly converted into electrical (then heat) energy in the tube rather than entirely into kinetic energy, so the magnet accelerates less. (1 mark) Markers reward both the Lenz's-law opposing-force statement and the energy-conversion link.