An Overview of Lenz’s Law

Lenz’s law is more or less based on Faraday’s law of guidance. Faraday’s law states that electric current in a conductor is induced by magnetic fields that are constantly changing. Lenz’s law indicates the direction of this induced current. This opposes a change in the magnetic field that created it. The change is indicated by a negative sign (‘–’) in equations given by Faraday’s law. 

Lenz’s equation

The changes observed in a magnetic field can be due to the altering strength of this magnetic field. This change may be due to the movement of a magnet – closer or further away, or as a result of the movement of the coil – inside and outside the magnetic field.

The equation below signifies that the electromotive force (ε) induced in a coil and the rate with which the magnetic flux (ΦB) changes have mathematically opposite signs.

                                  ε = – dΦB /dt 

Definition of Lenz’s law

In Lenz’s law of electromagnetic induction, the change in the magnetic field induces a current in the inductor in such a way that the magnetic field created by the induced current opposes the initial change in the magnetic field. We can find the direction of this current flow with the help of the right-hand rule given by Fleming.

Lenz’s law equation

The magnetic field change may be caused by the change in strength caused by moving a magnet to and fro or moving the coil inside and outside the magnetic field. 

According to Lenz’s law, a change in the magnetic flux causes an EMF to be induced (stated in Faraday’s law). The polarity of the EMF that is induced is such that it causes a current to be produced. This electric current is opposed by the source of its creation.

The law of electromagnetic induction, given by Faraday, tells us that the negative sign signifies an EMF (ε) induced in the coil and a change in its magnetic flux ( δΦB). Both these physical quantities have opposite signs and are, thus, opposing in nature. 

We can write the formula of Lenz’s law as follows:

                                                  ε = N δΦB /δt 

 Where

 ε denotes the emf induced in the coil 

 δΦB denotes the coil’s change in its magnetic flux 

 N denotes the number of turns in the coil 

Relating Lenz’s law and conservation of energy 

Lenz’s law is said to be a direct derivative of the conservation of energy law. According to this law, the direction of the current induced via Lenz’s law creates a magnetic field that opposes the field that created it. 

Let us consider a scenario when that was not the case.

• Let the magnetic field created by the induced current be in the same direction as the field that produced it. This would result in these two fields combining and creating a larger magnetic field.]

• The combined magnetic field would then induce another current, which is double the amount of current inside the conductor

• Hence, creating a magnetic field, which again induces another current, creates an infinite positive feedback loop.
• This violates the conservation of energy law. This law also follows the third law of motion given by Newton (i.e. there is always an equal and opposite reaction to every action)
• Therefore, if the induced current produces a magnetic field that is equal (and opposite in nature) to the magnetic field’s direction, then it can only resist the changing magnetic field in the environment

Understanding Lenz’s law

To better understand Lenz’s law, we take up two case scenarios. 

Case 1: When the magnet moves towards the coil’s side 

• The magnetic flux associated with the coil rises as the magnet’s north pole starts approaching the coil
• A magnetic field is formed when a change in the magnetic flux results in current being induced in the coil, according to the law of electromagnetic induction by Faraday
• According to Lenz’s law, this generated magnetic field across the coil either opposes itself or it will resist an increase in magnetic flux
• This is only possible when the approaching side of the coil achieves north polarity, as similar poles are known to repel

Case 2: When the magnet moves in a direction opposite to the coil

• The magnetic flux associated with the coil reduces as the magnet’s north pole moves away from the coil
• According to the law of electromagnetic induction by Faraday, an EMF, and subsequently an electric current, is induced in the coil, which produces its magnetic field
• This magnetic field formed, according to Lenz’s law, cancels itself or cancels the drop in magnetic flux travelling through the coil
• Because distinct poles attract one another, this is only possible when the approaching side of the coil achieves south polarity.

Fleming’s right-hand rule

The right-hand rule is used to find the magnetic field’s direction or current. When we wrap our right finger around the wire with our thumb pointing in the direction of the electric current, the finger curl points in the magnetic field’s direction generated by the wire.

Lenz’s law: Applications

The application of Lenz’s law is as follows: 

• The concept of magnetic energy, stored in inductors, is explained with the help of Lenz’s law
• When an EMF source is linked to both ends of an inductor, current flows through it. The opposing EMF tries to oppose the increase in the flow of current through the inductor. Some work needs to be done by the stored EMF to overcome the opposing nature of the back EMF
• This can be accomplished by storing the EMF in the inductor, which can then be restored when the external source of the EMF has been removed from the circuit.

• This law demonstrates that the generated EMF and the flux change have opposing signs. Thus, we get a physical explanation for the signs used in the law of induction (by Faraday)

• Generators are likewise subject to Lenz’s law. According to Lenz’s law, the direction of induced current in an electric generator is in such a way that it tries to oppose and cause the generator’s rotation. As a result, the generator necessitates additional mechanical power. Electric motors also provide EMF in the reverse direction.

• Electromagnetic brakes and inductive cooktops both use Lenz’s law.

Conclusion

In conclusion, we can state that the Lenz’s law is as follows:

• Whenever there is an increase in the magnetic flux (Ф) linked to a coil, electric current will flow in a direction that is going to oppose any increase in the flux.]
• The electric current that is induced is then going to produce magnetic flux. The direction of flux (Ф) is demonstrated in the diagram below. This is based on the right-hand thumb rule (by Fleming)

• When the magnetic flux connecting the coils drops, the magnetic flux generated by the current helps to support the main magnetic flux
• Thus, a current is going to flow in a direction.