Lenz's law

Connection with Law of Conservation of Energy

Another way of looking at Lenz's law is based on the principle of conservation of energy. When the magnet is moved towards the loop, the field due to the induced current in the loop exerts a force that opposes 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. Which means that we must exert a greater force inorder to continue pushing the magnet towards the loop. Suppose that if the current was produced in the oppsoite direction then the south pole of the induced magnetic field will be in the direction of the north pole of the magnet, due 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 is clearly a violation of law of conservation of energy.

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Therefore the induced emf should be produced in such a way that it opposes the cause producing it i.e. the change in magnetic flux. Furthermore the emf induced (back emf) in the coil is in the opposite direction to the supply emf, because if this wasn?t the case, the emf would increase the current, and the motor coil would go faster, and faster, creating energy indefinitely without further input of energy, hence violating the law of conservation of energy. This means that the induced emf must oppose the supply emf.

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

Related Topics:
Electromagnetic induction - Maxwell's equations

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