Lenz's Law: Definition, Formula, Applications & Faraday's Law

Lenz’s law is based on both the principle of conservation of energy and Newton’s third law. It is the most convenient method to determine the direction of the induced current. In electromagnetism, Lenz's law states that an induced electric current passes in a direction in a way that the current opposes the induced change. Lenz’s law simply defines the direction of the induced current that is seen to oppose the initial changing magnetic field which generated it.

Also Check: Uses of Inductor

Key Terms: Lenz Law, Ampere, Faraday’s Law, Electromagnetic Induction, Electromotive force, Galvanometer, Magnetic Flux, Joule’s Effect

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Faraday’s Law of Electromagnetic Induction

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Faraday’s law of electromagnetic induction, also known as Faraday’s law, is part of the law of electromagnetism that helps aid the prediction of how a magnetic field is going to interact with an electric circuit in order to produce an Electromotive Force (EMF). This phenomenon is also called Electromagnetic Induction.

After a series of experiments, it is concluded by Michael Faraday that some kind of force i.e. electromotive force, is generated in a coil when magnetic flux passing through the coil changes with time.

Faraday’s Law of Electromagnetic Induction Detailed Explanation

Faraday’s Laws of Electromagnetic Induction Video Explanation

Read Also: Magnetic Properties of Material

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What is Lenz’s Law?

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Lenz’s law is given by a physicist of Germany named Heinrich Friedrich Lenz. He described the direction of electric current relative to the magnetic flux. He deduced that the direction of an induced current in a circuit is such as to oppose the change that causes it.

Lenz law can be expressed as:

“The induced electromotive force that has different polarities induces a form of current which has a magnetic field opposing the change in magnetic flux via the loop to guarantee that the original flux has been maintained via the loop when current passes.”

Lenz Law Experiment

Apparatus: Take a coil connected to a galvanometer. Now as the North Pole of a bar magnet comes towards the coil it shows a deflection.

Observations: Three observations can be deducted from the above experiment:

1. In the stationary position of the magnet, Galvanometer shows no deflection.
2. When the magnet is pulled away from the coil, the deflection in the galvanometer is in the opposite direction, which means a reversal of the current’s direction.
3. Deflection is larger when the bar magnet is pulled towards or pushed away from the coil faster.

Through this activity, Lenz’s law comes into effect.

It can be concluded that current due to induced emf produces magnetism such that it opposes the cause producing it.

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Lenz’s Law Formula

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Lenz’s Law can be demonstrated as per the formula of Faraday’s law. In the formula, the given negative sign gives Lenz’s law. The expression is as followed:

Here,

• Emf = induced voltage (or called, electromotive force)
• N = Number of loops
• Δϕ = Change in magnetic flux
• Δt = Change in time

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Lenz’s Law and Conservation of Energy

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As per the experiment, the magnetic flux increases when the North Pole of the magnet comes towards it and decreases as it is pushed away.

First Case

In the first case, to oppose the cause means motion of the magnet, the face coming towards the coil acquires North Polarity.

The north pole of the magnet and the north pole of the coil repel each other. To move the magnet towards the coil, some sort of mechanical work has to be done to overcome the force of repulsion. This mechanical work is converted into electrical energy. This electrical energy is converted into heat energy due to Joule’s Effect.

Second Case

Similarly, when the magnet moves away from the coil, the nearer face of the coil acquires south polarity. In this case, the induced emf will oppose the outward motion of the magnet. Once again mechanical work has to be done to overcome the force of attraction between the North Pole of magnet and the South Pole of the coil. This work done is converted into electrical energy.

If the magnet is not moved, no mechanical work is done and then no emf is induced in the coil. Thus, this proves that Lenz’s Law is in accordance with the law of conservation of energy.

Lenz's Law and Electromagnetic Induction PDF

Read More: What are Electromagnets?

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Key facts about Lenz’s Law

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• In copper or aluminium pipes, a Counter-rotating current can be created by magnetic fields produced from strong magnets.
• This law demonstrates that induced emf and the change in flux have opposite signs which validate the choice of sign in Faradays’ Law of Induction.
• This law can also be applied to electric generators.
• The concept of Lenz’s Law can also be used to understand the basics of stored magnetic energy in an inductor.

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Applications of Lenz’s Law

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There are several applications of Lenz’s law, some include:

• Braking systems in trains,
• Metal detectors,
• Eddy current dynamometers,
• AC Generators,
• Card Readers,
• Microphones, etc.

Read More: Magnetism and Matter

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Previous Year Questions 

1.  If a transformer of an audio amplifier has output impedance 8000 0 and the speaker has input impedance…...[JCECE 2005]
2. A conducting loop in the shape of a right angled isosceles triangle of height 10cm10cm is kept such that the 90^∘ vertex is…..[JEE Advance 2016]
3. A 10m long horizontal wire extends from North East to South West. It is falling with a speed of 5.0ms⁻¹……. [ JEE Main 2019]
4. If a current of 2.0A2.0A flows through the smaller loop, then the flux linked with bigger loop is…… [JEE Main 2013]
5. A coil of cross-sectional area A having n turns is placed in a uniform magnetic field B….. [JEE Main 21018]
6. A copper rod of mass m slides under gravity on two smooth parallel rails, with separation ll and set at an angle of θ with the horizontal….. [JEE Main 2018]
7. A copper wire is wound on a wooden frame, whose shape is that of an equilateral…. [JEE Main 2019]
8. A metallic rod of length ll is tied to a string of length 2l and made to rotate with angular speed…. [JEE Main 2013]
9. A square frame of side 10 cm and a long straight wire carrying current 1 A are in the plane of the paper…. [JEE Main 2014]
10. If the rod makes n rotations per second, then the time averaged magnetic moment of the rod is… [JEE Main 2019]
11. Figure shows a circular area of radius R where a uniform magnetic field….
12. In a coil of resistance 100Ω , a current is induced by changing the magnetic flux through it….. [JEE Main 2017]
13. When current in a coil changes from 5A  to 2A…. [JEE Main 2015]
14. Which radiation in sunlight, causes heating effect? 
15. X -rays are….
16. Arrange the following in decreasing order of wavelength
17. Which is having minimum wavelength … [NEET 2002]
18. The speed of radio-waves is equal to… [JIPMER 1998]
19. Gamma rays and visible light waves rays are a,ba,b and cc respectively, then… [UPSEE 2016]

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Things to Remember

• Using Lenz’s law we can predict the direction of an induced emf caused by changing magnetic field through a loop or coil of wire.
• Lenz’s law can be explained using a loop and a moving bar magnet.
• This law is related to Faraday’s law of Electromagnetic induction and explains the negative sign in the formula of Faraday’s Law.
• Lenz’s law also validates the law of conservation of energy.

Read More: Experiment of Faraday and Henry