Lenz's law

Lenz's law (pronounced (IPA) ) was formulated by German physicist Heinrich Lenz in 1833 and gives the direction of the induced emf resulting from electromagnetic induction, thus:

The emf induced in an electric circuit always acts in such a direction that the current it drives around a closed circuit produces a magnetic field which opposes the change in magnetic flux.

Definition

The induced current produced in the conductor always flows in such a direction that the magnetic field it produces will oppose the change that is producing it.

Explanation

Lenz's Law states that in a given circuit with an induced EMF caused by a change in a magnetic flux, the induced EMF causes a current to flow in the direction that opposes the change in flux. That is, if a decreasing magnetic flux induces an EMF, the resulting current will oppose a further decrease in magnetic flux. Likewise, for an EMF induced by an increasing magnetic flux, the resulting current flows in a direction that opposes a further increase in magnetic flux.

It is important to note that the induced current will always flow in a direction which opposes any change of magnetic flux, but it does not oppose the magnetic flux itself.

Lenz's law can be derived from Faraday's law of induction, simply by noting the minus sign on the right side of the equation.

Connection with law of conservation of energy

Lenz's law is one consequence of the principle of conservation of energy. If a magnet moves towards a closed loop; then, the induced current in the loop creates a field that exerts a force opposing the motion of the magnet. The loop sets up a magnetic field similar to that of a magnet with its north pole pointing towards the north pole of the magnet, and the two north poles repel each other. Therefore a greater force must be exerted in order to continue pushing the magnet towards the loop.

Suppose instead that the current was produced in the opposite direction. Then the south pole of the induced magnetic field would be in the direction of the north pole of the magnet, to which the magnet would be accelerated by the field. As the magnet accelerates, the current in the loop would increase, causing an increasing force on the magnet and an increasing acceleration. Both the kinetic energy of the magnet and the rate of energy dissipation in the loop would increase. This means that for a very small push we would get a large energy dissipation which clearly violates the law of conservation of energy. Therefore the emf opposes the change that induces it, i.e. the change in magnetic flux.

See electromagnetic induction and Maxwell's equations for further mathematical treatment.

Electrodynamics | Eponymous laws

Gourt Home::Gourt :: Lenz's law

Definition

Explanation

Connection with law of conservation of energy