# Lenz’s law

Heinrich Friedrich Emil Lenz was a Russian physicist, working at the University of St. Petersburg, Russia. He formulated Lenz’s law in 1834. This law predicts the direction of the current and the induced voltage in a coil held in a magnetic field.

## Lenz’s law – Statement

The direction of an induced e.m.f. is always such that it tends to set up a current opposing the motion or the change of flux responsible for inducing that e.m.f.

EMF is induced in a coil when there is a relative motion between the coil and a magnetic field. So, according to this law, the direction of induced emf or current is always such that it opposes the change in the magnetic field. This may be a little difficult to understand in the beginning.

## Explanation

Assume that we have a coil and a permanent magnet. Here you must remember the following points.

• Change in the magnetic field (field-1) in a closed-loop cause electric current flow.
• As you know, current flow in a coil produces a magnetic perpendicular to the conductor. Hence the induced current produces its own magnetic field (field-2).

Lenz’s law states that the direction of the induced current will be such that the field-2 produced by it opposes field-1.

As you notice in the above illustration, when the permanent magnet (Field-1) is moved towards the coil, an EMF is induced in it which produces a current(I). The polarity of EMF will be such that the magnetic field (Field-2) produced by the current(I) opposes the further motion of Field-1 towards it.

Similarly, when the permanent magnet is moved away from the coil, the polarity of the induced EMF will be such that Field-2 opposes the motion of Field-1 away from it.

Here the motion of permanent magnet’ is the cause and the direction of induced current sets up a magnetic field that opposes the motion of the permanent magnet.

Lenz’s law can be considered as a magnetic corollary to Newton’s third law (Every action has an equal and opposite reaction) and the law of conservation of energy. The change in the magnetic field is an action and the direction of the induced current is the reaction.

## Lenz’s law equation

Lenz’s law is based on Faraday’s law of electromagnetic induction. The combined equation for these two laws are:

Where, N is the number of turns of coil, ΔΦ is the change in magnetic flux through the coil in time Δt. The minus sign indicates the opposition to the change in magnetic field.

## Experiment explaining Lenz law

The above experiment shows two aluminium rings suspended on a pivot such that they can move freely in the horizontal plane. One of the rings has an opening and does not form a complete circle. When a bar magnet is brought closer to the enclosed ring, it is repulsed by the magnet. In this case, the induced current resists the further change increase in magnet flux. When the magnet is pulled back, the ring is attracted by it. In this case, the induced current resists the decrease in magnet flux.

This phenomenon is absent when the bar magnet is moved towards or away from the non enclosed ring since the induced current cannot enclose the magnet.