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

• 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 a permanent magnet and a coil in front of it, with the north pole nearest the coil, and place a small camera on the north end 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 emphasized. 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.

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.

Practical demonstrations

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

• A dramatic demonstration of the effect with an aluminium block in an MRI, 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.

Lenz's Law states that the induced emf and the change in Flux linkage has opposite directions. Experiment:

The experiment to prove this is that when we enter a magnet in a coil with current passing through it the magnet will induce a same pole and will repel it but when we try to take the magnet out then it will induce an opposite pole which will attract it causing a change in the flux Linkage.

External links

• Eddy Currents and Lenz's Law (Audio slideshow from the National High Magnetic Field Laboratory)