Lenz’s law and Faraday’s law of electromagnetic induction

Lenz’s law:-



Lenz’s law is named after the German scientist H. F. E. Lenz in 1834. Lenz’s law obeys Newton’s third law of motion (i.e to every action there is always an equal and opposite reaction) and the conservation of energy (i.e energy may neither be created nor destroyed and therefore the sum of all the energies in the system is a constant)
Lenz law is based on Faraday’s law of induction so before understanding Lenz’s law one should know what Faraday’s law of induction is "When a changing magnetic field is linked with a coil, an emf is induced in it. This change in magnetic field may be caused by changing the magnetic field strength by moving a magnet toward or away from the coil or moving the coil into or out of the magnetic field as desired".

Heinrich Friedrich Emil Lenz

LENZ’S LAW

Lenz law states that when an emf is generated by a change in magnetic flux according to Faraday’s Law, the polarity of the induced emf is such that it produces a current whose magnetic field opposes the change which produces it.
The negative sign is used in Faraday’s law of electromagnetic induction, indicates that the induced emf ( ε ) and the change in magnetic flux ( δΦ_B ) have opposite signs.

Where
ε = Induced emf
δΦ_B = change in magnetic flux
N = No of turns in coil

Reason for opposing, cause of induced current in Lenz’s law?

• As stated above Lenz law obeys the law of conservation of energy and if the direction of the magnetic field that creates the current and the magnetic field of the current in a conductor are in same direction, then these two magnetic field would add up and produce the current of twice the magnitude and this would in turn creates more magnetic field, which cause more current and this process continues on and on and thus leads to violation of the law of conservation of energy.
• If the induced current creates a magnetic field which is equal and opposite to the direction of magnetic field that creates it, then only it can resist the change in the magnetic field in the area which is in accordance to the Newton’s third law of motion

EXPLANATION OF LENZ’S LAW

For understanding Lenz’s law consider two cases :

CASE-I When a magnet is moving towards the coil. 



When the north pole of the magnet is approaching towards the coil, the magnetic flux linking the coil increases. According to Faraday’s law of electromagnetic induction, when there is change in flux, an emf and hence current is induced in the coil and this current will creates its own magnetic field . Now according to Lenz law, this magnetic field created will oppose its own cause or we can say opposes the increase in flux through the coil and this is possible only if approaching coil side attains north polarity, as we know similar poles repel each other. Once we know the magnetic polarity of the coil side, we can easily determine the direction of the induced current by applying right hand rule. In this case the current flows in anticlockwise direction.

CASE-II When a magnet is moving away from the coil.


 
When the north pole of the magnet is moving away from the coil, the magnetic flux linking the coil decreases. According to Faraday’s law of electromagnetic induction, an emf and hence current is induced in the coil and this current will creates its own magnetic field . Now according to Lenz’s law, this magnetic field created will oppose its own cause or we can say opposes the decrease in flux through the coil and this is possible only if approaching coil side attains south polarity, as we know dissimilar poles attract each other. Once we know the magnetic polarity of the coil side, we can easily determine the direction of the induced current by applying right hand rule. In this case the current flows in clockwise direction.

NOTE : For finding the directions of magnetic field or electric current use Right hand thumb rule i.e if the fingers of the right hand are placed around the wire so that the thumb points in the direction of current flow, then the curling of fingers will show the direction of the magnetic field produced by the wire.

Right hand thumb rule

The Lenz law can be summarized as under:

• If the magnetic flux Ф linking a coil increases, the direction of current in the coil will be such that it oppose the increase in flux and hence the induced current will produce its flux in a direction as shown below (using right hand thumb rule).

• If magnetic flux Ф linking a coil is decreasing, the flux produced by the current in the coil is such that it aid the main flux and hence the direction of current is as shown below

APPLICATION OF LENZ’S LAW

• Lenz law can be used to understand the concept of stored magnetic energy in an inductor. When a source of emf is connected across an inductor, a current starts flowing through it. The back emf will oppose this increase in current through the inductor. In order to establish the flow of current, the external source of emf has to do some work to overcome this opposition. This work done by the emf is stored in the inductor and it can be recovered after removing the external source of emf from the circuit
• This law indicates that the induced emf and the change in flux have opposite signs which provide a physical interpretation of the choice of sign in Faraday’s law of induction.
• Lenz’s law is also applied to electric generators. When an electric current is induced in a generator, the direction of this induced current is such that it opposes its cause i.e rotation of generator (as in accordance to Lenz’s law) and hence the generator requires more mechanical energy. It also provides back emf in case of electric motors.
• Lenz’s law is also used in electromagnetic braking and induction cook tops.

Faraday’s law of electromagnetic induction

In 1831, Michael Faraday, an English physicist gave one of most basic law of electromagnetism called Faraday’s law of electromagnetic induction. This law explains the working principle of most of electrical motors, generators, electrical transformers and inductors. This law shows the relationship between electric circuit and magnetic field. Faraday performs an experiment with a magnet and coil. During this experiment he found how emf is induced in the coil when flux linked with it changes. He has also done experiments in electrochemistry and electrolysis.

Michael Faraday

Faraday’s Experiment

RELATIONSHIP BETWEEN INDUCED EMF AND FLUX

Faraday’s law

In this experiment Faraday takes a magnet and a coil and connects a galvanometer across the coil. At starting the magnet is at rest so there is no deflection in the galvanometer i.e needle of galvanometer is at centre or zero position. When the magnet is moved toward the coil, the needle of galvanometer deflects in one direction. When the magnet is held stationary at that position, the needle of galvanometer returns back to zero position. Now when the magnet is moved away from the coil , there is some deflection in the needle but in opposite direction and again when the magnet become stationary at that point with respect to coil , the needle of galvanometer return back to zero position. Similarly if magnet is held stationary and the coil is moved away and towards the magnet, the galvanometer shows deflection in similar manner. It is also seen that the faster the change in the magnetic field, the greater will be the induced emf or voltage in the coil.

Position of magnet	Deflection in galvanometer
Magnet at rest	No deflection in galvanometer
Magnet moves towards the coil	Deflection in galvanometer in one direction
Magnet is held stationary at same position (near the coil)	No deflection in galvanometer
Magnet moves away from the coil	Deflection in galvanometer but in opposite direction
Magnet is held stationary at same position (away from the coil)	No deflection in galvanometer

CONCLUSION: From this experiment Faraday concluded that whenever there is relative motion between conductor and a magnetic field, the flux linkage with a coil changes and this change in flux induces a voltage across a coil.

Michael Faraday formulated two laws on the basis of above experiments. These laws are called Faraday’s laws of electromagnetic induction.

Faraday’s Laws

Faraday’s First Law

Any change in the magnetic field of a coil of wire will cause an emf to be induced in the coil. This emf induced is called induced emf and if the conductor circuit is closed, the current will also circulate through the circuit and this current is called induced current.
Method to change magnetic field:
1. by moving a magnet toward or away from the coil
2. by moving the coil into or out of the magnetic field.
3. by changing area of a coil placed in the magnetic field
4. by rotating the coil relative to the magnet.

Faraday’s Second Law

It states that the magnitude of emf induced in the coil is equal to the rate of change of flux linkages with the coil. The flux linkages of the coil is the product of number of turns in the coil and flux associated with the coil.

Faraday Law Formula

Faraday’s law

Consider a magnet approaching towards a coil. Here we consider two instants at time T₁ and time T₂.
Flux linkage with the coil at time, T₁ = NΦ₁ Wb
Flux linkage with the coil at time, T₂ = NΦ₂ wb
Change in flux linkage = N(Φ₂ – Φ₁)
Let this change in flux linkage be, Φ = Φ₂ – Φ₁
So, the Change in flux linkage = NΦ
Now the rate of change of flux linkage = NΦ / t
Take derivative on right hand side we will get
The rate of change of flux linkage = NdΦ/dt
But according to Faraday’s law of electromagnetic induction the rate of change of flux linkage is equal to induced emf.




Considering Lenz’s Law





Where flux Φ in Wb = B.A
B = magnetic field strength
A = area of the coil

HOW TO INCREASE EMF INDUCED IN A COIL

• By increasing the number of turns in the coil i.e N- From the formulae derived above it is easily seen that if number of turns of coil is increased, the induced emf is also increased.
• By increasing magnetic field strength i.e B surrounding the coil- Mathematically if magnetic field increases, flux increases and if flux increases emf induced will also increased Theoretically if the coil is passed through a stronger magnetic field, there will be more lines of force for coil to cut and hence there will be more emf induced.
• By increasing the speed of the relative motion between the coil and the magnet. – If the relative speed between the coil and magnet is increased from its previous value, the coil will cut the lines of flux at a faster rate so more induced emf would be produced.

Applications of Faraday Law

Faraday law is one of the most basic and important law of electromagnetism . This law finds its application in most of electrical machines, industries and medical field etc.

• Electrical Transformers
It is a static ac device which is used to either step up or step down voltage or current. It is used in generating station, transmission and distribution system. The transformer works on Faraday’s law.

• Electrical Generators
The basic working principle of electrical generator is Faraday’s law of mutual induction .Electric generator is used to convert mechanical energy into electrical energy.

• Induction Cookers
The Induction cooker, is a most fastest way of cooking. It also works on principle of mutual induction. When current flows through the coil of copper wire placed below a cooking container, it produces a changing magnetic field. This alternating or changing magnetic field induces an emf and hence the current in the conductive container and we know that flow of current always produces heat in it.

• Electromagnetic Flow Meters
It is used to measure velocity of blood and certain fluids. When a magnetic field is applied to electrically insulating pipe in which conducting fluids are flowing then according to Faraday’s law an electromotive force is induced in it. This induced emf is proportional to velocity of fluid flowing .

• Form the bases of Electromagnetic Theory
Faraday’s idea of lines of force is used in well known Maxwell’s equations. According to Faraday’s law change in magnetic field gives rise to change in electric field and the converse of this is used in Maxwell’s equations.

• Musical Instruments
It is also used in musical instruments like electric guitar, electric violin etc.