Lenz’s law states that the direction of an induced current is such that its magnetic effect opposes the change in magnetic flux that produced it. It gives the minus sign in Faraday’s law and follows from conservation of energy.
Learning objectives
- State Lenz’s law and explain its link to energy conservation.
- Determine the direction of an induced current for a changing flux.
- Explain why a generator becomes harder to turn under load.
- Recognise Lenz’s law effects in eddy-current braking and induction machines.
Progressive explanation
Start with the plain-language idea, then move into the engineering detail. Each level stands on its own, so you can stop at the depth you need.
Beginner The core idea
This opposition is not accidental: it follows from energy conservation. If the induced current helped the change instead of opposing it, energy would be created from nothing. The mechanical work you do pushing the magnet is converted into electrical energy in the coil, which is exactly how a generator produces power.
Intermediate How it behaves in a circuit
For a conductor moving in a magnetic field, Lenz’s law predicts a force opposing the motion. This braking effect is used in eddy-current brakes and is also the reason a generator becomes harder to turn as its electrical load increases. In both cases, the mechanical power absorbed equals the electrical power delivered plus losses.
Advanced Limits, assumptions, engineering detail
Eddy currents in conducting masses obey Lenz’s law and produce drag; laminated cores reduce these losses by limiting the loops available to eddy currents. In magnetic levitation and induction motors, the same principle produces useful forces. At high frequency, the opposition is not only resistive but also reactive, and the phase between flux and induced current determines whether the effect is braking or energy storage.
Formulas and variables
Units of measurement
| Quantity | Symbol | Unit |
|---|---|---|
| Magnetic flux | Φ | weber (Wb) |
| Induced EMF | EMF | volt (V) |
| Magnetic force | F | newton (N) |
| Power | P | watt (W) |
Worked examples
Direction and magnitude of an induced EMF
Problem. A 50-turn coil sees its flux increase from 0.020 Wb to 0.060 Wb in 0.10 s. Find the induced EMF and state its direction effect.
Solution. ΔΦ = 0.060 − 0.020 = 0.040 Wb, so EMF = −50 × 0.040/0.10 = −20 V. The magnitude is 20 V; the minus sign means the induced current creates a flux opposing the increase.
Opposing force on a moving conductor
Problem. A 0.30 m conductor carrying 2.0 A induced current sits in a 0.50 T field perpendicular to its length. What magnetic force acts on it?
Solution. F = B × I × l = 0.50 × 2.0 × 0.30 = 0.30 N. By Lenz’s law the force opposes the motion that produced the induced current.
Practical applications
- Generators and regenerative braking
- Eddy-current brakes and dampers
- Transformers and coupled coils
- Induction motors and electromagnetic launchers
Automotive applications
Regenerative braking in electric and hybrid vehicles uses Lenz’s law: the traction motor is driven as a generator, and the induced current produces a braking force while charging the battery. In conventional vehicles, eddy-current retarders use the same principle to slow heavy vehicles without friction brakes, and the drag increases with speed and field strength.
Industrial applications
Eddy-current separators sort non-ferrous metals by inducing currents that are repelled by a magnetic field. Induction furnaces use induced currents to melt metal in a crucible, and induction motors rely on induced rotor currents to produce torque. In all these applications, the direction of the induced effect follows Lenz’s law, which determines whether the machine brakes, drives or heats.
Measurement procedure
- When observing induced current direction, note the winding direction and the probe polarity; a small change in coil orientation reverses the effect.
- An oscilloscope shows the phase relationship between flux change and induced voltage, which reveals the opposition described by Lenz’s law.
- For rotating machines, compare mechanical input power with electrical output power to verify that the induced effect opposes the driving motion.
- Remember that the induced EMF appears even when no current flows; Lenz’s law concerns the direction current would take in a closed circuit.
Common mistakes
- Thinking the induced current always flows in the same direction; it reverses when the flux change reverses.
- Forgetting that Lenz’s law concerns opposition to the change, not opposition to the field itself.
- If there is no closed path, the induced EMF has no current direction to oppose, though the EMF still exists.
- Confusing the induced magnetic field direction with the external field direction rather than with the change in flux.
Safety considerations
- Inductive kickback can produce high voltages when current is interrupted; fit suppression diodes or other clamps where appropriate.
- Eddy-current and magnetic braking systems can become hot; allow them to cool before inspection.
- Strong magnetic fields can attract tools and metal objects; keep magnetic-sensitive devices and implants away.