Lenz Law

What is Lenz’s Law?

Lenz’s Law named after the physicist Emil Lenz was formulated in 1834. It states that the direction of the current induced in a conductor by a changing magnetic field is such that the magnetic field created by the induced current opposes the initial changing magnetic field.

When a current is induced by a magnetic field, then the magnetic field produced by the induced current will create its magnetic field. Thus, this magnetic field will be opposed by the magnetic field that created it. 

Lenz law is based on Faraday's law of Induction which says, a changing magnetic field will induce a current in a conductor whereas, Lenz's law tells us the direction of induced current, which opposes the initial changing magnetic field which produced it. Hence, this is signified in the formula for Faraday's law by the negative sign.

\[\epsilon = - \frac{d\Phi_{B}}{dt}\]

The magnetic field can be changed by changing its strength or by either moving the magnet towards or away from the coil, or moving the coil in or out of the magnetic field.

Hence we can say that the magnitude of the electromagnetic field induced in the circuit is proportional to the rate of change of flux.

\[\varepsilon \propto \frac{d\Phi}{dt}\].

Lenz Law Formula:

According to Lenz's law, when an electromagnetic field is generated by a change in magnetic flux, the polarity of the induced electromagnetic field produces an induced current whose magnetic field opposes the initial changing magnetic field which produced it.

The formula for Lenz law is shown below:

\[\epsilon = - N \frac{\partial \Phi_{B}}{\partial t}\]


ε = induced EMF

δΦ =  change in magnetic flux

N = number of turns in the coil

Lenz law applications:

The Applications of Lenz's Law Include:

  1. When a source of an electromagnetic field is connected across an inductor, a current starts flowing through it. The back electromagnetic field will oppose this increase in current through the inductor. To establish the flow of current, the external source of the electromagnetic field has to do some work for overcoming this opposition.

  2. The Lenz’s law is used in electromagnetic brakes and induction cooktops.

  3. It is also applied to electric generators, AC generators.

  4. Eddy Current Balances

  5. Metal detectors

  6. Eddy current dynamometers

  7. Braking systems on train

  8. Card Readers

  9. Microphones

Lenz Law Experiment:

To find the direction of the induced electromotive force and current we use Lenz’s law. Some experiments are below.

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First Experiment:

In the first experiment, when the current in the coil flows in the circuit, the magnetic field lines are produced. As the current flows through the coil increases, the magnetic flux will increase. The direction of the flow of induced current would be such that it opposes when the magnetic flux increases.

Second Experiment:

In the second experiment, when the current-carrying coil is wound on an iron rod with its left end behaving as N-pole and is moved towards the coil S, an induced current will be produced.

Third Experiment:

In the third experiment, the coil is pulled towards the magnetic flux, the coil linked it goes on decreasing that means that the area of the coil inside the magnetic field decreases. 

According to Lenz’s law, the motion of the coil is opposed when the induced current is applied in the same direction.

To produce current, force is exerted by the magnet in the loop. To oppose the change a force must be exerted by the current on the magnet.