Lenz's law

Lenz's law


A law of electromagnetism which states that, whenever there is an induced electromotive force (emf) in a conductor, it is always in such a direction that the current it would produce would oppose the change which causes the induced emf. If the change is the motion of a conductor through a magnetic field, the induced current must be in such a direction as to produce a force opposing the motion. If the change causing the emf is a change of flux threading a coil, the induced current must produce a flux in such a direction as to oppose the change.


Definition

Lenz's law states that induced e.m.f. opposes the change in flux producing it.

Connection with law of conservation of energy

Lenz's Law is one consequence of the principle of conservation of energy. To see why, move a permanent magnet towards the face of a closed loop of wire (eg. a coil or solenoid). An electric current is induced in the wire, because the electrons within it are subjected to an increasing magnetic field as the magnet approaches. This produces an emf (Electromotive Force) that acts upon them. The direction of the induced current depends on whether the north or south pole of the magnet is approaching: an approaching north pole will produce an anti-clockwise current (from the perspective of the magnet), and south pole approaching the coil will produce a clockwise current.

To understand the implications for conservation of energy, suppose that the induced currents' directions were opposite to those just described. Then the north pole of an approaching magnet would induce a south pole in the near face of the loop. The attractive force between these poles would accelerate the magnet's approach. This would make the magnetic field increase more quickly, which in turn would increase the loop's current, strengthening the magnetic field, increasing the attraction and acceleration, and so on. Both the kinetic energy of the magnet and the rate of energy dissipation in the loop (due to Joule heating) would increase. A small energy input would produce a large energy output, violating the law of conservation of energy.

This scenario is only one example of electromagnetic induction. Lenz's Law states that the magnetic field of any induced current opposes the change that induces it.

For a rigorous mathematical treatment, see electromagnetic induction and Maxwell's equations.

Practical Demonstrations

A brief video demonstrating Lenz's Law is at EduMation.

A neat device made by William J. Beaty levitates a magnet above two spinning rollers.

A dramatic demonstration of the effect with an aluminum block in an MRI, falling very slowly.

A demonstration that even a small child can try:
- Find a small electric motor.
- Spin its shaft.
- Connect its wires together (with a paper clip or alligator clip), and spin the shaft again.
- This time, the motor resists turning, because current can flow through its wires.