Lenz's law

Electromagnetism

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Lenz's law (pronounced /ˈlɛntsɨz ˌlɔː/) is an extension of the law of conservation of energy to the non-conservative forces in electromagnetic induction. It can be used to give the direction of the induced electromotive force (emf) and current resulting from electromagnetic induction. Heinrich Lenz postulated in 1834 the following law;

"An induced current is always in such a direction as to oppose the motion or change causing it"

The law provides a physical interpretation of the choice of sign in Faraday's law of induction, indicating that the induced emf and the change in flux have opposite signs.

Explanation of Lenz's law

If the magnetic field associated with the current in a conductor were in the same direction as the change in magnetic field that created it, these two magnetic fields would combine to give a net magnetic field which would in turn induce a current with twice the magnitude. This process would continue creating infinite current from just moving a magnet: this would be a violation of the law of conservation of energy.

Taking a permanent magnet and putting a coil in front of it, with the north pole nearest the coil, as the magnet is brought closer to the coil, this will increase the flux through the coil. Then, by Lenz's law, the current will be in counterclockwise direction from the north end of the magnet when looking into the coil from the south pole of magnet. If the magnet is brought away from the coil, this will decrease the flux through the coil. Therefore, the current should be induced in the clockwise direction from the north end of the magnet. By keeping at rest but increasing the field strength of the magnet, the flux through the coil will be increased: thus the induced current should be in the counterclockwise direction from the north end of the magnet. This case is analogous to the case where we moved the magnet towards the coil. Similarly, if the magnet is kept at rest but the field strength of the magnet decreases, the current will be induced in the clockwise direction from the aforementioned position.

Another possible situation is increasing the area of the coil. In this case, the flux through the coil is increased, so that a current is induced by Faraday’s law. Increasing the area of the coil is in fact equivalent to bringing the magnet closer to the coil; both cases effectively increase the magnetic flux through the coil. Therefore, the current will be induced in the counterclockwise direction from the north end of the magnet. Decreasing the area of the coil is equivalent to bringing the magnet away from the coil since both cases effectively decrease the flux through the coil. Therefore, decreasing the area of the coil will induce a current in the clockwise direction.

Connection with law of conservation of energy

The law of conservation of energy relates exclusively to irrotational (conservative) forces. Lenz's Law extends the principles of energy conservation to situations that involve non-conservative forces in electromagnetism. To see an example, move a 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 (electro-motive 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 a counter-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.

External links

• Eddy Currents and Lenz's Law (Audio slideshow from the National High Magnetic Field Laboratory)
• EduMation A brief video demonstrating Lenz's Law
• A dramatic demonstration of the effect with an aluminium block in an MRI