Lenz's law

From Wikipedia, the free encyclopedia

All or part of this article may be confusing or unclear. Please help clarify the article. Suggestions may be on the talk page. (February 2008)

This article does not cite any references or sources. (March 2008) Please help improve this article by adding citations to reliable sources. Unverifiable material may be challenged and removed.

Lenz's law (pronounced /ˈlɛntsɨz ˌlɔː/) gives the direction of the induced electromotive force (emf) and current resulting from electromagnetic induction. 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. Heinrich Lenz formulated the law in 1834.

[edit] Definition

Lenz's law states that the induced current in a loop is in the direction that creates a magnetic field that is parallel to the change in magnetic flux through the area enclosed by the loop. That is, the induced current tends to keep the original magnetic flux through the field from changing. This law is an example of Le Chatelier's principle of equilibriums, which also involves a system resisting a change in its original state when disturbed.

[edit] 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 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 (electromagnetic field) 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.

[edit] 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 aluminium block in an MRI, falling very slowly.

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