Lenz's law

Lenz's law (pronEng|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.

It is a special case of Le Chatelier's principle in its general form: "Any change in status quo prompts an opposing reaction in the responding system." This law is often quoted as a joke to describe any phenomenon in life happening in exactly the opposite way to the one desired.

Applications and Examples

* The following is an explanation as to why Lenz's law is true: If the magnetic field associated with this current 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; a violation of the law of conservation of energy.

* Take the north pole of a permanent magnet and a coil in front of it and put a microscopic camera on top of the magnet. As you bring the magnet closer to the coil, you are increasing the flux through the coil. Then by Lenz's law, the current will be in counterclockwise direction as viewed by the camera.

* If you bring the magnet away from the coil, you are decreasing the flux through the coil. Therefore, the current should be induced in the clockwise direction as viewed from the camera.

* What if you keep the magnet at rest but increase the field strength of the magnet? In this case you are increasing the flux through the coil. Now one must read Lenz's law carefully:

The current associated to this emf will be such that the flux it creates opposes the change in flux that created it.

Notice that change in flux is printed in bold. Increasing the field strength of the magnet just means that the change in flux is towards the coil so that Lenz's law tells us that the induced current should be in the counterclockwise direction as viewed from the camera. Note that this case is analogous to the case where we moved the magnet towards the coil.

* Similarly, if we keep the magnet at rest but decrease the field strength of the magnet, the current will be induced in the clockwise direction as viewed by the camera.

* Another possible situation is increasing the area of the coil. In this case, we are increasing the flux through the coil so that a current is induced by Faraday’s law. Note that increasing the area of the coil is 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 as viewed by the camera.

* 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.

* Note how we always specified the direction of the induced current with reference to the camera. In general, physics pays a lot of importance to reference frames.

* See the article on Faraday's law of induction

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 (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 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 [http://msdaif.googlepages.com/demo_lenz EduMation] .

A neat device made by William J. Beaty [http://www.youtube.com/watch?v=glCNP6qH_Dc levitates a magnet] above two spinning rollers.

A dramatic demonstration of the effect with an aluminium block in an MRI, [http://youtube.com/watch?v=fxC-AEC0ROk falling very slowly] .

A demonstration that illustrates Lenz's law is:

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.