Lenz's Law

Lenz's law is named after the German scientist H. F. E. Lenz in 1834. Lenz's lawobeys 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. Or in simple words we can say that the magnitude of the emf induced in the circuit is proportional to the rate of change of flux.

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 an electric 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 ( δΦB ) have opposite signs.

Where
ε = Induced emf
δΦB = 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 toFaraday'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.