Lenz's law

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Lenz's law (pronounced (IPA) [ˈlɛntsəz lɔ]) was formulated by German physicist Heinrich Lenz in 1834 and gives the direction of the induced electromotive force (emf) and current resulting from electromagnetic induction.

[edit] Definition

For a current induced in a conductor, the current is in such a direction that its own magnetic field opposes the change that produced it.

[edit] Connection with law of conservation of energy

Lenz's Law is one consequence of the principle of conservation of energy. To understand why, consider a permanent magnet that is moved 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 gets closer and this produces an emf that acts upon them. The direction of the induced current will depend on whether it is the north pole or the south pole of the magnet that is approaching: an approaching north pole will produce an anti-clockwise current (from the perspective of the magnet) while an approaching south pole will produce a clockwise current.

Circulating currents produce their own magnetic fields, of course, due to electromagnetism: the anti-clockwise current will produce a north pole on this face and the clockwise current a south pole. Note that in both cases the induced electromagnetic pole is of the same kind as the magnet that produced it. The two north poles will repel each other, as would two south poles. In both cases, the induced current produces a magnetic field, and therefore a force, that opposes the approach of the very magnet that created it.

The same will be true when the magnet is withdrawn, ie. moved away from the loop. The magnetic field is now decreasing, so the induced currents will be reversed. The electromagnetically induced poles are now of the same kind as the receding magnet's so the two will attract. Once again, the induced fields are opposing the change that created them, in this case a receding magnet.

To understand the implications for conservation of energy, suppose that the above description was not true and that the induced currents were produced in the opposite directions to those described. Then, for example, the north pole of an approaching magnet would induce a south pole in the nearest face of the loop. The attractive force between them would accelerate the magnet's approach, and this would make the magnetic field increase more quickly. This would increase the current in the loop, which would produce a stronger induced magnetic field, a bigger force of attraction, yet more 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, to move the magnet forward, would produce a large energy output, which clearly violates the law of conservation of energy.

The above scenario is only one example of electromagnetic induction. Lenz's Law ensures that all induced currents have magnetic fields that oppose the change that induces them.

See electromagnetic induction and Maxwell's equations for a more rigorous mathematical treatment.