Lenz's law - Definition, Formula and Experiments

Conceived and formulated by the Russian physicist Heinrich Friedrich Emil Lenz in 1834, Lenz’s law states that an electric current induced in a conductor as a result of changing the magnetic field flows in a direction such that the current opposes the change in the magnetic field that induced it in the first place. The basis for Lenz’s law depends on the principle of conservation of energy and Newton’s third law. Lenz’s law is very helpful in determining the direction of the induced current as, according to the law, the direction of the induced current is opposite to that of the magnetic field. However, Lenz’s law does not describe anything about the magnitude of the value of the induced electric current.

- Let us consider a coil of wire made from a conductive metal.
- A permanent magnet is taken, and any one of its poles is pushed through into the coil of wire. The magnetic field of the permanent magnet induces an electric current in the coil. This induced current creates another magnetic field around the coil, turning the coil of wire into a magnet.
- Since similar poles of two magnets tend to repel each other, as the north pole of the permanent magnet approaches the coil of wire, the induced current will change its direction of flow in order to make the side of the coil which is near to the approaching permanent magnet, turn into the north pole so that it can repel the north pole of the permanent magnet.
- However, if the north pole of the permanent magnet is moved away from the coil of wire, the induced current switches its direction of flow to its original.
- Now, that side of the coil becomes a south pole and attracts the north pole of the permanent magnet. This happens so that the total magnetic flux in the system remains constant. This was given and explained by Lenz’s law.
- The effort taken in pushing the permanent magnet inside the coil and pulling it out against the magnetic field constitutes a small quantity of work done. The energy needed for this work to be done gets released into the system as heat. This is further proof that Lenz’s law is in accordance with the principle of conservation of energy.

Lenz’s law can be expressed using the following expression of Faraday’s law.

ɛ = −N (Δϕ/ Δt)

where

ɛ is the induced electromotive force
N is the number of windings in the coil
Δϕ is the change in the magnetic field
Δt is the change in time
(Δϕ/ Δt) is the rate of change in magnetic flux with respect to the time.
The negative (-) sign is a result of Lenz’s law, signifying the direction of flow of the induced electric current.

From the above equation, it can be determined that the magnitude of the induced electromotive force is directly proportional to the rate of change of magnetic flux. That is

ε ∝ (Δϕ / Δt)

Another example where Lenz’s law explains the change in magnetic flux is when a permanent magnet is dropped inside a solid pipe made of either copper or aluminium. It can be noticed that despite the magnet being dropped vertically inside the pipe, its motion is much slower inside but resumes a faster falling motion when it is outside the pipe.

As per Faraday’s law, the change in magnetic flux brings about a voltage in the pipe. This created voltage induces an electric current. The polarity of the voltage is such that the magnetic field produced due to the induced current opposes the change created in the original magnetic field. This magnetic field constantly tries to keep the magnitude of the magnetic flux constant inside the pipe. The motion of the permanent magnet inside the tube is slowed down due to these reasons. Fleming's right-hand rule can determine the direction of the induced current, magnetic field, and magnetic flux.

Experiments of Lenz’s Law

To prove the basis and validity of his law, Lenz performed certain experiments that served as proof of his hypothesis. The three experiments and his conclusions from each are discussed below.

- First experiment: Magnetic field lines are produced in a conductor when an electric current flows through it. As the magnitude of the current increases, the magnetic flux also increases correspondingly. However, the direction of flow of the current is opposite to that of the magnetic flux.

- Second experiment: A conductive coil was wound over an iron rod, and an electric current was passed through the coil. The left end served as the north pole, and when it was moved towards the coil, an induced current was produced.

- Third experiment: To produce an induced current, the magnetic field exerts a force on the coil, and in turn, a force is exerted by the electric current on the magnetic field, opposing it.