Lenz's law

Lenz's law says that the direction of an induced current is always such that it opposes the change that produced it. Push the north pole of a magnet into a coil, and the induced current makes the near end of the coil a north pole too, pushing back against the magnet. Pull the magnet out, and the near end becomes a south pole, pulling against it. Lenz's law tells you which way the induced emf acts, and Faraday's law, ε = N ΔΦ ÷ Δt, tells you how big it is.

What Lenz's law says

Whenever the magnetic flux through a circuit changes, an emf is induced. If the circuit is complete, a current flows. Lenz's law says that current always flows in the direction that fights the change: it creates its own magnetic field, or its own force, in the opposite sense to whatever caused it.

AQA's GCSE Physics specification describes the generator effect this way: an induced current generates a magnetic field that opposes the original change, either the movement of the conductor or the change in magnetic field. At A-level, AQA's specification covers Faraday's and Lenz's laws together.

Faraday's law and the minus sign

How big is the induced emf? Faraday's law says it equals the rate of change of flux linkage. AQA's data booklet gives:

Lenz's law is often shown by putting a minus sign in front, ε = −N ΔΦ ÷ Δt. The minus sign means the induced emf acts against the change in flux. When you are only asked for the size of the emf, leave the sign out and use Lenz's law separately to find the direction.

A magnet and a coil

A quicker push, a stronger magnet or more turns on the coil all give a bigger induced current, but its direction is always the one that opposes the motion.

Why Lenz's law must be true: conservation of energy

Suppose the induced current did the opposite and helped the change. Pushing a magnet into a coil would then attract it in, making it move faster, inducing a bigger current, pulling it in harder still. You would get electrical energy and kinetic energy from nothing. That would break conservation of energy. Because the induced current opposes the change, you have to do work to keep the magnet or the conductor moving, and that work is where the electrical energy comes from.

Lenz's law worked examples

Example 1: size and direction in a coil

A coil of 200 turns links a flux that falls from 3.0 × 10⁻⁴ Wb to 1.0 × 10⁻⁴ Wb in 0.050 s. Find the average induced emf, and say which way the induced current's field points.

The flux is decreasing, so by Lenz's law the induced current makes a field in the same direction as the original field, trying to keep the flux from falling.

Example 2: a rod moving along rails

A metal rod 0.25 m long slides at a steady 4.0 m/s along two rails, at right angles to a 0.30 T magnetic field. The rails and rod form a circuit with total resistance 1.5 Ω. Find the emf, the current and the force on the rod.

Each second the circuit's area grows by lv, so the flux grows by Blv each second:

The current is I = 0.30 ÷ 1.5 = 0.20 A. That current sits in a magnetic field, so the rod feels a force F = BIl = 0.30 × 0.20 × 0.25 = 0.015 N. Lenz's law tells you this force acts against the motion: to keep the rod moving at constant speed, you must push it with 0.015 N.

Check the energy: the power you supply is Fv = 0.015 × 4.0 = 0.060 W, and the power dissipated in the circuit is I²R = 0.20² × 1.5 = 0.060 W. They match, as conservation of energy requires.

Lenz's law in everyday technology

• Magnetic braking: a metal disc or rail moving through a magnetic field has currents induced in it (eddy currents). By Lenz's law, they produce forces that oppose the motion, slowing it without contact.
• A magnet falling through a copper tube falls much more slowly than through a plastic one. The changing flux induces currents in the copper that oppose the magnet's fall.
• Generators get harder to turn when more current is drawn from them. The bigger induced current produces a bigger opposing force, and that extra work is the extra electrical energy supplied.

Finding the direction in a moving conductor

For a wire moving through a field, Fleming's right-hand rule gives the direction of the induced current: thumb for motion, first finger for field, second finger for current. Then check with Lenz's law: the force on that current, from Fleming's left-hand rule, should point against the motion. If it does not, you have made a mistake. Our guide to magnetic flux density and magnetic flux covers B, Φ and flux linkage.

The Field Lines Simulator lets you place magnets and see their fields, which helps when picturing how the flux through a coil changes.

Try it

Field Lines Simulator

Place charges and magnets and see their electric and magnetic fields

Open the simulatorGo to its page

Here is a quick check.

Common mistakes

• Saying the induced field always opposes the magnet's field. It opposes the change in flux. If the flux is falling, the induced field points the same way as the original, to keep it up.
• Forgetting the energy argument. In "explain" questions, linking Lenz's law to conservation of energy often earns a mark.
• Mixing up the hand rules. Right hand for generators (induced current); left hand for motors (force on a current).
• Including the minus sign in a magnitude. When asked for the size of the emf, give a positive value.

Practise fields in a short timed paper

A-level Physics: Year 2 and GCSE Physics Higher each give you a short timed paper every day, with 8 questions worth 25 to 35 marks across the course, so electromagnetic induction turns up regularly but not in every paper. In AQA's A-level, Faraday's and Lenz's laws are taught in the second year.

Read next

Physics · Fields and gravityCoulomb's law: F = kQ₁Q₂/r² explained, with examplesCoulomb's law F = Q₁Q₂ ÷ 4πε₀r² explained: the constants, attraction and repulsion, the inverse square law, worked examples and a comparison with gravity.