Lenzs Law - Definition, Formula, Examples, Applications, FAQs

Edited By Team Careers360 | Updated on Jul 02, 2025 04:31 PM IST

Lenz Law:

Lenz law is associated with, named after Emil Lenz, is based on the conservation of energy principle and Newton's third law. It is the most practical way for determining the induced current's direction. It asserts that the direction of an induced current is always in opposition to the circuit or magnetic field change that causes it.

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Lenz Law:
State Lenz law of electromagnetic induction and define Lenz law.
Lenz law formula:
Lenz Law Examples:
Applications of Lenz law

Lenzs Law - Definition, Formula, Examples, Applications, FAQs

State Lenz law of electromagnetic induction and define Lenz law.

Lenz Law Definition or Lenz Law Statement: “When current runs through the loop, the induced electromotive force with various polarities produces a current whose magnetic field oppose change in magnetic flux through loop, ensuring that the original flux is preserved.”

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Lenz law formula:

The formula of Faraday's law is based on Lenz's law. Lenz law provides the negative sign in this case. It is given by the formula:

$$
\mathrm{Emf}=-\mathrm{N}(\Delta \phi / \Delta \mathrm{t})
$$
The induced voltage is referred to as Emf (also known as electromotive force).

The number of loops is N .
$\Delta \phi$ shift in the magnetic flow
$\Delta t$ is the passage of time.

The induced electromotive force and the rate of change in magnetic flux have the same sign, indicating that they are in opposing directions.

This indicates that the direction of an induced field's back EMF opposes the changing current that causes it. D.J. Griffiths summed it up this way: "Nature despises change."

It's a qualitative law that describes the direction of generated current but not the amplitude of it. Many electromagnetic phenomena, such as the direction of voltage induced in an inductor by changing current, or the drag force of eddy currents imparted on moving objects in a magnetic field, are predicted by Lenz law.

Lenz Law Examples:

In a copper or aluminum pipe, large magnetic fields can cause counter-rotating currents. Dropping the magnet through the pipe demonstrates this. When the magnet is dropped within the pipe, it descends at a slower rate than when it is dropped outside the pipe.

According to Faraday's law, when a voltage is formed by a change in magnetic flux, the induced voltage's polarity produces a current whose magnetic field opposes change which is produced by itself. The magnetic flux in any loop of wire is always kept constant by the induced magnetic field inside the loop.

The right-hand rule can be used to determine the direction of an induced current, which shows which direction of current flow creates a magnetic field that opposes the direction of changing flux through the loop. When the flux is growing in the instances below, the induced field opposes it. If it is decreasing, the induced field opposes the change by acting in the same direction as the applied field.

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Applications of Lenz law

Lenz has a plethora of legal uses. The following are a few of them:

Balances of eddy currents
Metal detectors are used to detect metal.
Eddy current dynamometers.
Train AC generators have braking systems.
Readers of credit cards
Microphones

Experiment of Lenz law of electromagnetic induction:

Lenz law is used to determine the direction of the induced electromotive force and current. In accordance with Lenz's theory, he performed some experiments.

lenz law of electromagnetic induction

NCERT Physics Notes:

The Initial Experiment

He concluded in the first experiment that magnetic field lines are formed when electricity in the coil flows in the circuit. The magnetic flux will grow as the current flowing through the coil increases. When the magnetic flux increases, the flow of induced current will be in the opposite direction.

Experiment number 2

In the second experiment, he discovered that an induced current is produced when the current-carrying coil is wound on an iron rod with its left end acting as an N-pole and advanced towards the coil S.

Experiment three

In the third experiment, he discovered that when the coil is drawn towards the magnetic flux, the coil connected to it shrinks, implying that the coil's area within the magnetic field shrinks. When the induced current is delivered in the same direction as the coil's motion, Lenz's law states that the coil's motion is opposed.

The magnet in the loop exerts a force on the current to produce it. The current must exert a force on the magnet to counteract the change.

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Frequently Asked Questions (FAQs)

1. How does Lenz law of energy conservation work?

Lenz law is based on the idea of energy conservation. The induced current is always resisted by the source that produces it, according to the definition of Lenz law. As a result, more effort is done against the opposing force. Work done against an opposing force causes a change in magnetic flux, which causes current to be produced. Electrical energy is the result of the extra labour done, and it is protected by the rule of conservation of energy.

2. What is the distinction between Lenz's and Faraday's laws?

Faraday's law is about the electromagnetic force created, whereas Lenz law is about energy conservation applied to electromagnetic induction.

3. What is the most crucial aspect of Lenz law?

The direction of the induced current is determined using Lenz law.

4. In Lenz law, what does the negative sign mean?

The induced emf in the coil is in the opposite direction of the magnetic flux that is coupled to the coil, as indicated by the negative sign in lenz law equation.

5. Where does Lenz law come into play?

Electromagnetic circuits obey the conservation of energy and Newton's third law, according to Lenz law.

6. How does Lenz's Law explain the concept of "back EMF" in electric motors?

Back EMF (electromotive force) in electric motors is a direct application of Lenz's Law. As the motor rotates, it acts like a generator, producing an induced voltage that opposes the applied voltage. This induced voltage, or back EMF, increases with the motor's speed, limiting the current and preventing the motor from accelerating indefinitely.

7. Why does a falling magnet through a copper tube fall slower than it would in free fall?

When a magnet falls through a copper tube, it induces eddy currents in the tube. According to Lenz's Law, these currents create a magnetic field that opposes the motion of the falling magnet. This opposing force slows the magnet's descent, making it fall slower than it would in free fall. This demonstration is a classic example of Lenz's Law in action.

8. How does Lenz's Law affect the efficiency of transformers?

Lenz's Law impacts transformer efficiency by causing some energy loss. The changing magnetic field in the primary coil induces a current in the secondary coil, but it also induces a back EMF in the primary coil itself. This back EMF opposes the original current, resulting in some energy being converted to heat. Transformer design aims to minimize these losses while maintaining the desired voltage transformation.

9. How does Lenz's Law explain the braking system in some electric vehicles?

In electric vehicles with regenerative braking, Lenz's Law plays a crucial role. When braking, the electric motor acts as a generator. The wheels' rotation creates a changing magnetic field, inducing a current in the motor windings. Lenz's Law ensures this current opposes the wheels' motion, providing a braking effect. This process also allows for energy recovery, charging the vehicle's batteries.

10. How does Lenz's Law contribute to the principle of energy conservation?

Lenz's Law ensures that induced currents always flow in a direction that opposes the change causing them. This opposition requires energy, which comes from the original source of the changing magnetic field. By creating this resistance, Lenz's Law prevents the creation of energy from nothing, thus upholding the principle of energy conservation.

11. Why doesn't a stationary magnet induce a current in a nearby stationary coil?

Lenz's Law (and electromagnetic induction in general) requires a change in magnetic flux to induce a current. A stationary magnet near a stationary coil doesn't create any change in magnetic flux. Without this change, there's no induced EMF or current. This illustrates that it's not the magnetic field itself, but the change in magnetic flux that's crucial for induction.

12. How does Lenz's Law explain the difficulty in pushing a strong magnet into a copper coil?

When you push a magnet into a copper coil, the changing magnetic field induces a current in the coil. According to Lenz's Law, this induced current creates its own magnetic field that opposes the motion of the magnet. This opposition manifests as a force you can feel, making it difficult to push the magnet in. The stronger the magnet or the faster you try to push it, the stronger this opposing force becomes.

13. Can Lenz's Law be used to explain why superconductors exhibit perfect diamagnetism?

Yes, Lenz's Law helps explain perfect diamagnetism in superconductors. When a magnetic field is applied to a superconductor, it induces surface currents. According to Lenz's Law, these currents create a magnetic field that exactly cancels the applied field inside the superconductor. This perfect opposition results in the expulsion of magnetic flux from the superconductor's interior, known as the Meissner effect.

14. What role does Lenz's Law play in the operation of induction cooktops?

In induction cooktops, Lenz's Law is fundamental to the heating process. The cooktop generates a rapidly changing magnetic field. When a ferromagnetic pot is placed on the cooktop, this changing field induces eddy currents in the pot's base. Lenz's Law dictates that these currents flow in a way that opposes the change causing them, resulting in resistance and heat generation within the pot itself.

15. How does Lenz's Law affect the design of electromagnetic shielding?

Electromagnetic shielding relies on Lenz's Law to protect sensitive equipment from external electromagnetic fields. When an external field penetrates the shield, it induces currents according to Lenz's Law. These currents generate a counter magnetic field that opposes and cancels out the external field. Effective shielding materials are good conductors that allow these induced currents to flow freely.

16. What is Lenz's Law and how does it relate to electromagnetic induction?

Lenz's Law states that the direction of an induced current in a conductor is such that it opposes the change that caused it. In electromagnetic induction, when a changing magnetic field induces a current in a conductor, Lenz's Law determines the direction of this induced current. It's nature's way of conserving energy and is a consequence of the law of conservation of energy.

17. Why doesn't a perfect conductor allow any magnetic field to penetrate its interior?

In a perfect conductor, any change in external magnetic field would induce currents on its surface instantaneously. According to Lenz's Law, these currents would create a magnetic field that exactly cancels the change inside the conductor. As a result, the net magnetic field inside a perfect conductor remains constant (usually zero if it started that way). This is similar to the behavior of superconductors, demonstrating perfect diamagnetism.

18. How does Lenz's Law explain the phase difference between voltage and current in an inductor?

In an inductor, Lenz's Law causes the induced EMF to oppose changes in current. When an AC voltage is applied, the changing current induces a back EMF that lags behind the applied voltage. This results in the current lagging behind the voltage by 90 degrees in an ideal inductor. The phase difference is a direct consequence of Lenz's Law opposing the change in current.

19. Why does a copper ring placed around an iron core in a transformer reduce its efficiency?

A copper ring around a transformer's iron core acts as a shorted turn. When the magnetic field changes, it induces a current in this ring according to Lenz's Law. This current creates its own magnetic field that opposes the core's field, reducing the overall magnetic flux and the transformer's efficiency. This is why transformer cores are typically laminated rather than solid, to minimize such eddy current effects.

20. How does Lenz's Law contribute to the concept of self-inductance?

Self-inductance occurs when a changing current in a circuit induces an EMF in the same circuit. Lenz's Law dictates that this self-induced EMF opposes the change in current that caused it. This opposition to change is what gives an inductor its characteristic property of resisting changes in current flow. The magnitude of this effect is determined by the inductance of the circuit.

21. What is the formula for Lenz's Law, and what do the symbols represent?

The formula for Lenz's Law is often expressed as ε = -N(dΦ/dt), where:

22. Why does a rapidly changing magnetic field heat up a nearby conductor?

A rapidly changing magnetic field induces eddy currents in a nearby conductor, as per Faraday's Law. Lenz's Law ensures these currents flow in a way that opposes the change in the magnetic field. These induced currents encounter resistance in the conductor, leading to Joule heating. The more rapid the field change and the more conductive the material, the greater the heating effect.

23. How does Lenz's Law contribute to the skin effect in conductors carrying high-frequency AC?

The skin effect, where high-frequency AC tends to flow near the surface of a conductor, is partly explained by Lenz's Law. As current flows, it creates a magnetic field. Changes in this field induce eddy currents within the conductor. Lenz's Law ensures these currents flow to oppose the change, effectively pushing the main current towards the conductor's surface. This effect becomes more pronounced at higher frequencies.

24. How does Lenz's Law explain the operation of a magnetic brake system?

In a magnetic brake system, a conductor (often a metal disc) moves through a magnetic field. This motion induces eddy currents in the conductor. Lenz's Law dictates that these currents create a magnetic field opposing the motion, resulting in a braking force. The faster the motion, the stronger the induced currents and the greater the braking effect, making it an effective speed-dependent braking system.

25. Can Lenz's Law be used to explain why it's harder to pull a magnet out of a coil than to push it in?

Yes, Lenz's Law explains this asymmetry. When pushing a magnet into a coil, the induced current creates a field opposing the motion, making it feel resistant. When pulling it out, the induced current still opposes the change, now creating a field that tries to keep the magnet in the coil. This attractive force, combined with the effort to overcome it, often makes pulling the magnet out feel harder than pushing it in.

26. Can you explain the relationship between Faraday's Law and Lenz's Law?

Faraday's Law describes the magnitude of the induced EMF in a conductor exposed to a changing magnetic field, while Lenz's Law determines the direction of the induced current. Together, they provide a complete description of electromagnetic induction. Lenz's Law is often considered a consequence or extension of Faraday's Law.

27. How does Lenz's Law relate to the concept of mutual inductance between two coils?

In mutual inductance, a changing current in one coil induces a voltage in a nearby coil. Lenz's Law determines the direction of the induced current in the second coil. This induced current will always flow in a direction that opposes the change in the first coil's magnetic field. This opposition is crucial in understanding how energy is transferred between the coils and in designing transformers and other coupled inductors.

28. Why does a metal ring jump up when a strong electromagnet beneath it is suddenly turned on?

When the electromagnet is suddenly turned on, it creates a rapidly changing magnetic field. This changing field induces a current in the metal ring according to Faraday's Law. Lenz's Law then dictates that this induced current flows in a direction that creates a magnetic field opposing the change. The result is a repulsive force between the ring and the electromagnet, causing the ring to jump up.

29. How does Lenz's Law contribute to the damping of oscillations in a swinging magnet pendulum over a conducting plate?

As a magnet pendulum swings over a conducting plate, its changing position induces eddy currents in the plate. Lenz's Law ensures these currents create a magnetic field opposing the pendulum's motion. This opposing force acts as a damping mechanism, gradually reducing the pendulum's amplitude. The energy of the pendulum's motion is dissipated as heat in the conducting plate due to these induced currents.

30. How does Lenz's Law affect the rise time of current in an inductor?

When a voltage is applied to an inductor, the changing current creates a changing magnetic field. Lenz's Law dictates that this changing field induces a back EMF in the inductor that opposes the change in current. This opposition slows the rate at which current can increase, leading to a gradual rise in current rather than an instantaneous jump. This effect is characterized by the inductor's time constant.

31. Can Lenz's Law be used to generate electricity from ocean waves?

Yes, Lenz's Law is applicable in wave energy converters. One design involves a floating magnet moving inside a coil as waves pass. The magnet's motion relative to the coil creates a changing magnetic field, inducing a current in the coil according to Lenz's Law. While Lenz's Law dictates that this induced current will oppose the magnet's motion (creating some damping effect on the waves), it's this very current that can be harnessed as electrical energy.

32. Can Lenz's Law be used to explain why transformers don't work with DC current?

Yes, Lenz's Law helps explain why transformers don't work with DC current. Transformers rely on electromagnetic induction, which requires a changing magnetic field. With DC, the magnetic field in the primary coil is constant, so no EMF is induced in the secondary coil. Lenz's Law only comes into play with changing fields, which is why transformers require AC to function.

33. Can Lenz's Law be used to explain why a magnet falling through a copper tube reaches a terminal velocity?

Yes, Lenz's Law explains this phenomenon. As the magnet falls, it induces eddy currents in the copper tube. Lenz's Law ensures these currents create a magnetic field opposing the magnet's motion. The faster the magnet falls, the stronger these opposing currents become. Eventually, the magnetic force upward equals the gravitational force downward, resulting in a terminal velocity.

34. How does Lenz's Law explain the behavior of a Faraday cage?

A Faraday cage protects its interior from external electric fields. When an external field is applied, it induces charges on the cage's surface. Lenz's Law ensures these induced charges create a field that opposes the external field. The result is that the fields cancel out inside the cage. While Lenz's Law primarily deals with magnetic fields, this analogous behavior with electric fields demonstrates the broader principle of induced effects opposing their cause.

35. How does Lenz's Law affect the design of electric generators?

Lenz's Law significantly impacts generator design. As the generator produces electricity, the induced current creates a magnetic field that opposes the rotation of the generator (back EMF). This opposition requires more mechanical power to overcome as more electrical power is drawn. Generator designs must account for this effect, balancing factors like rotor speed, field strength, and load to optimize efficiency and power output.

36. Why doesn't a changing electric field induce a magnetic field according to Lenz's Law?

Lenz's Law specifically deals with induced currents from changing magnetic fields, not changing electric fields. However, a changing electric field does induce a magnetic field, as described by Maxwell's equations. This is not a direct application of Lenz's Law, but rather a fundamental aspect of electromagnetism. Lenz's Law is more about the direction of induced currents from magnetic field changes.

37. How does Lenz's Law explain the phase shift between the primary and secondary coils in a transformer?

In an ideal transformer, there is no phase shift between primary and secondary voltages. However, in real transformers, Lenz's Law contributes to a small phase shift. The changing current in the primary induces a voltage in the secondary, but it also induces a back EMF in the primary itself. This self-inductance causes a slight phase lag in the primary current, which can result in a small phase difference between primary and secondary voltages.

38. Can Lenz's Law be used to explain the concept of mutual inductance in wireless charging systems?

Yes, Lenz's Law is crucial in understanding wireless charging. In these systems, an alternating current in the primary coil creates a changing magnetic field. This field induces a current in the secondary coil (in the device being charged) according to Lenz's Law. The induced current in the secondary opposes the change causing it, which is the basis for energy transfer. The efficiency of this transfer depends on factors like coil design and alignment.

39. How does Lenz's Law contribute to the stability of magnetic levitation systems?

In magnetic levitation systems, Lenz's Law provides a stabilizing effect. If an object being levitated moves from its equilibrium position, it experiences a changing magnetic field. This change induces currents that, according to Lenz's Law, create a magnetic field opposing the motion. This opposition tends to push the object back towards its equilibrium position, providing stability to the levitation system.

40. Why does a metal detector's sensitivity decrease when it's moved too quickly over a metal object?

Metal detectors work by creating a changing magnetic field that induces eddy currents in metal objects. When moved too quickly, the rapid field change induces stronger currents in the metal object, as per Lenz's Law. These stronger currents create a more powerful opposing magnetic field, which can actually reduce the net change in the detector's field, potentially making the object harder to detect. Optimal detection usually requires a moderate, steady scanning speed.

41. How does Lenz's Law explain the operation of a Hall effect sensor?

While Hall effect sensors primarily rely on the Lorentz force, Lenz's Law plays a role in their dynamic behavior. When a changing magnetic field is applied, it induces eddy currents in the sensor's conductor. Lenz's Law ensures these currents create a magnetic field opposing the change. This can affect the sensor's response time and sensitivity, especially in rapidly changing fields, and must be considered in sensor design and signal processing.