Lenz’s Law

Introduction

Electricity and magnetism were initially separate subjects. Electricity was related to the charges and magnetism was related to the magnetic materials only. However in the 19th century a Danish physicist, Oersted demonstrated that there is a relation between these two. He found that electric current can create a magnetic field around them.

Michael Faraday the British experimental scientist reported one interesting phenomenon. He found that if we move a magnet around a coil connected to a galvanometer, we see deflection in that.

The presence of the current in the circuit in such cases implies that an electromotive force gets induced in the circuit when we change the magnetic field around it. This phenomenon is called electromagnetic induction. The amount of induced electromotive force is given by faraday’s law. It says that the rate of change of magnetic flux is equal to the induced electromotive force in the circuit. However, if we want to know the direction of the current induced in the circuit due to electromagnetic induction, we use another law. It is called Lenz’s law.

What is Lenz's Law?

In, 1834 Emil Lenz a Russian physicist gave a law that helps us to get the direction of induced current. It is known as Lenz’s law.

It says - If a current is induced inside a conductor it will also create a magnetic field around it. The direction of the current will be such that the magnetic field created by it will oppose the change that induced it. For better understanding, let us take an example.

MikeRun, Lenzs-law-cylindrical-magnet-leaving-ring, CC BY-SA 4.0

Fig:1 Illustration of Lenz’s law

Suppose there is a circular conductor as shown in the figure above. A bar magnetic is approaching it from the left. The moving bar magnet will induce a current in the conductor. We can see that the current creates a magnetic field that is clockwise and the original field due to the bar magnet was anticlockwise. Hence the magnetic field due to the induced current is opposing the source of the induced current.

The Formula for Lenz's Law

Lenz’s law says that the current or emf will, will oppose the change in the magnetic flux since the change in the magnetic flux is the reason for this induced emf. If the magnetic field is given by B, and magnetic flux is $\mathrm{\phi _{B}}$. Then

$$\mathrm{e=-N\frac{d\phi _{B}}{dt}}$$

N = no. of loops

dt = change in time

Here negative sign is crucial since it tells us about the direction. The word “oppose” is contained in the sign. If we want to only the magnitude of the induced emf, then we can write it like this

$$\mathrm{\left|e \right|\propto \frac{d\phi _{B}}{dt}}$$

What is Induced EMF?

When the magnetic flux of a conductor changes, an emf gets induced in it. It is known as induced emf. Suppose there is a coil with N loops, and it is slowly rotating in the magnetic field, then an emf will be induced in it. The amount of induced emf can be given by Faraday’s law. If the magnetic field is B, and the flux dphi is changing for time dt. Then induced emf

$$\mathrm{e =-N \frac{d\phi _{B}}{dt}}$$

Experiment with Lenz's law

Lenz formulated his law theoretically. His theory was proved by the following three experiments.

Keministi, Lenz law demonstration, CC0 1.0

First Experiment

In the first experiment, when the current flows in the circuit, a magnetic field gets created around it. As we increase the current, the magnetic flux increases since the magnetic field depends upon the current. The current opposes any change in the magnetic flux.

Second Experiment

In the second experiment, he found that, if we take a current carrying wire and wound it over an iron rod, then the one end of it behaves like the North pole and it gets attracted toward the south pole of the magnet. Hence an induced current gets generated.

Third Experiment

In the third experiment, when the coil is dragged in the direction of the magnetic flux, the area of the coil inside the field decreases. Lenz’s law tells us that if we apply the induced current in the same direction the motion of the coil is opposed.

For this, the magnetic field exerts a force on the coil. In opposition, a magnetic force is exerted by the current of the coil on the magnetic field.

Applications

It is used in the following areas.

• Card readers, microphones, and AC generators.

• It tells us the magnetic energy stored in the inductors.

• This concept is used in metal detectors and baking systems of trains

• It gives the physical understanding of the minus sign present in faraday’s formulation.

• It is used in eddy current dynamometers and balances.

Conclusion

Electromagnetic induction is a phenomenon when a change in flux creates an emf in a conductor. The amount of induced emf can be given by faraday’s law. The direction of induced emf or current is given by Lenz's law. It says the induced emf has a direction such that it opposes any change arising in the flux. It is useful in many technological applications. Its prominence can be seen almost in each place where the electromagnetic induction phenomenon is used.

FAQs

Q1. Which conservation law justifies Lenz’s law?

Ans. Lenz’s law is a direct consequence of the conservation of energy(electrical).

Q2. The magnetic flux of a coil is given by $\mathrm{\phi _{B}=B_{0}A\:sin\omega t}$, find the expression for the induced emf.

Ans. We know that the induced emf is $\mathrm{e =-N \frac{d\phi _{B}}{dt}}$

$$\mathrm{e =-N \frac{d}{dt}(B_{0}A\:sin\omega t)=-NB_{0}A\:{\omega}cos(\omega t)}$$

Q3. circular ring of radius 10cm lies parallel to the magnetic field. The magnetic field changes from 35mT to 60mT in 200ms. Find the magnitude of the induced emf.

Ans. It is given that the radius $\mathrm{r=10\times 10^{-2}m}$

Also the magnetic flux $\mathrm{\phi _{B}=B\pi r^{2}}$, since B and A are parallel to each other.

$$\mathrm{Induced \:emf\:\left|e \right|=\frac{d}{dt}\phi _{B}=\frac{d}{dt}(B\pi r^{2})}$$

$$\mathrm{=\pi r^{2}\frac{dB}{dt}=\pi r^{2}\frac{(B_{2}-B_{1})}{t}}$$

$$\mathrm{\left|e \right|=\pi r^{2}\frac{25}{200}=\pi (10^{-2})(0.125)}$$

$$\mathrm{\left|e \right|=0.3925\times 10^{-2}V=3.9mV}$$

Q4. For induced emf, is it necessary that the magnetic field should be changing?

Ans. No, the magnetic field does’t need to changing always. The net magnetic flux should change. For example, there can be a situation where the magnetic field is not changing but the area vector might be changing. Even in this situation, we can get induced emf.

Q5. What are the types of inductions, describe briefly.

Ans. Induction can be of two types

• Mutual Induction:- In this kind of induction, we need two coils near each other and magnetic flux change in one coil can lead to an induced emf in the other one.

• Self-Induction:- In this kind of induction, we need only one coil. Here the coil itself induces an emf to oppose the change in the strength of the current.