Faraday's Law of Electromagnetic Induction

Faraday's Law of Electromagnetic Induction

Edited By Vishal kumar | Updated on Jul 02, 2025 04:29 PM IST

Faraday's discovery of electromagnetic induction laid the foundation for electrical engineering. Faraday's law also describes the nature of induced electromotive force in a conductor in the presence of a magnetic field. In this article, we will discuss Micahel Farady discovery, Faraday's first law of electromagnetic induction, Faraday's second law of electromagnetic induction, derivation of Faraday's law, explanation of Faraday’s experiments, and applications of Faraday’s Law.

This Story also Contains
  1. Michael Faraday Discovery
  2. Faraday's First Law of Electromagnetic Induction
  3. Faraday’s 2nd Law
  4. Derivation of Faraday's Law
  5. Explanation of Faraday’s Experiments
  6. Faraday's First Experiment
  7. Faraday's Second Experiment
  8. Faraday’s Law of Electromagnetic Induction
  9. Applications of Faraday’s Law
Faraday's Law of Electromagnetic Induction
Faraday's Law of Electromagnetic Induction

Michael Faraday Discovery

Michael Faraday FRS was an English scientist who made significant contributions to the fields of electrochemistry and electromagnetism. The principles underpinning electromagnetic induction, diamagnetism, and electrolysis were among his most important discoveries.
Michael faraday

Michael Faraday conducted substantial research on electrolysis of electrolyte solutions and melts. He was the first scientist to describe the Laws of Electrolysis in quantitative terms. He developed two laws to explain the quantitative characteristics of electrolysis, which are today known as Faraday’s laws of electrolysis, namely the first and second laws of electrolysis.

Faraday's First Law of Electromagnetic Induction

“Whenever a conductor is put in a fluctuating magnetic field, an electromotive force is induced,” according to Faraday's first law of electromagnetic induction. A current is induced when the conductor circuit is closed, and this is known as an induced current.”

$$
\mathcal{E}=-\frac{d \Phi_B}{d t}
$$

where,

  • $\mathcal{E}$ is the induced EMF
  • $\Phi_B$ is the magnetic flux
  • $\frac{d \Phi_B}{d t}$ is the rate of change of magnetic flux

Faraday’s 2nd Law

The induced emf in a coil is equal to the rate of change of flux linkage

$$
\mathcal{E}=-N \frac{d \Phi_B}{d t}
$$

where,

  • $\mathcal{E}$ is the induced EMF
  • $N$ is the number of turns in the coil
  • $\Phi_B$ is the magnetic flux through the circuit
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Derivation of Faraday's Law

Magnetic flux is given as

$\Phi_B=\int \vec{B} \cdot d \vec{A}$

For a uniform magnetic field vector

$\Phi_B=B \cdot A \cdot \cos \theta$

Differentiating both sides to get the rate of change of magnetic flux

$\frac{d \Phi_B}{d t}=\frac{d}{d t}(B \cdot A \cdot \cos \theta)$

Substituting terms we get

$\mathcal{E}=-N \frac{d \Phi_B}{d t}$

For a coil of N turns

$$
\mathcal{E}=-N \frac{d \Phi_B}{d t}
$$

Explanation of Faraday’s Experiments

What is the Electromagnetic Induction Experiment, and how does it work?

The mechanism through which a current can be made to flow due to a magnetic field transition is known as electromagnetic induction.

Experiment by Michael Faraday

In 1831, Faraday observed that when the number of magnetic field lines in a circuit changes, an induced EMF is formed in the circuit, a process known as electromagnetic induction. The current runs through the circuit when it is closed, and this is known as the induced current. While the magnetic flux fluctuates, the induced EMF and electric current endure only a short time. Faraday and Henry are two examples of this type of work.

Faraday's First Experiment

  1. A closed circuit with an insulated wire coil.
  2. Also, because there is no source of EMF in the circuit, there is no deflection in the galvanometer.
  3. When we advance the bar magnet towards the coil while keeping the coil fixed (say), the needle of the galvanometer deflects, indicating the current pressure in the circuit.
  4. This deflection is only visible for the period of time that the magnet is moving. The galvanometer needle is now deflected in the other direction if we press the magnet in the opposite way.
  5. The deflection is now in the other direction if we move the magnet towards the coil with its south pole facing coil, suggesting that the current set in the coil is now in the opposite direction as when the north pole faces the wire.
  6. When the magnet is stationary and the circuit is moved away from the magnet, the galvanometer shows deflection.
  7. The velocity of the magnet is likewise observed to be higher, as is the deflection of the galvanometer needle.
  8. Faraday deduced from this experiment that moving the magnet in one direction toward the coil had the same effect as moving the coil in the opposite direction toward the magnet.

Faraday experiment no.1

Faraday's Second Experiment

  1. The deflection is now in the other direction if we move the magnet towards the coil with its south pole facing coil, suggesting that the current set in the coil is now in the opposite direction as when the north pole faces the wire.
  2. When the magnet is stationary along with the circuit moving away from the magnet, the galvanometer shows deflection.
  3. The velocity of the magnet is likewise observed to be higher, as is the deflection of the galvanometer needle.
  4. Faraday deduced from this experiment that moving the magnet in one direction toward the coil had the same effect as moving the coil in the opposite direction toward the magnet.

Faraday’s Law of Electromagnetic Induction

The creation of electromotive force across electrical conductors in a changing magnetic field is called magnetic induction. Induction was discovered by Michael Faraday in 1813 as well as it was mathematically characterized as Faraday’s law of induction by James Clerk Maxwell.

Electromagnetic Induction According to Faraday’s law:

  1. The time rate of change of magnetic flux in the circuit equals the magnitude of the induced emf in the circuit. The induced emf can be calculated using the formula $\mathcal{E}=-\frac{d \Phi_B}{d t}$.
  2. The negative sign indicates that the current generated in a circuit frequently flows in such a way that it opposes or causes the change.

In the case of a tightly wound N-turn coil, the flux change associated with each turn is identical. As a result, the expression for the total induced emf is -

$$
\varepsilon=-\mathrm{N}(\mathrm{~d} \phi / \mathrm{dt}) .
$$

Applications of Faraday’s Law

An electrical transformer is a common use of Faraday’s law. A transformer is made up of two independent coils wound around a piece of iron. The primary coil is one of two, while the secondary coil is the other. Due to Faraday’s law, this shifting field will induce a current in the secondary.

Faraday’s ring transformer

Other applications are:

  • Faraday’s ring transformer
  • Electric generators
  • Electromagnetic brakes
  • Metal Detectors

Also read:

Frequently Asked Questions (FAQs)

1. What exactly is a Faraday cage?

The Faraday is a non-measuring electric charge volume unit equivalent to about 6.02 x 10^23 electric charge carriers.

2. What is Faraday’s law and its significance?

According to Faraday’s law, a fluctuating magnetic flux generates an electric field. Faraday’s law is particularly essential since it deals with the E-field-B-field relationship and recognizes that this connection necessitates flux variation over time.

3. How does electrolysis work to get rid of rust?

Electrolysis is a technique for eliminating iron oxide that involves delivering a tiny electrical charge from a battery or battery charger through rusted metal to stimulate ion exchange while the device is submerged in an electrolyte solution.

4. In electrolysis, what is the name of the negative electrode?

The cathode is the negatively charged electrode created by electrolysis. In electrolysis, the positively charged electrode is known as the anode. Ions with a negative charge are travelling towards the anode.

5. According to faraday’s law EMF stands for what?

The force in any closed circuit due to a change in the flux linkage of the circuit is called electromotive force EMF, according to Faraday’s law.

6. What is Faraday's Law of Electromagnetic Induction?
Faraday's Law states that the induced electromotive force (EMF) in a closed loop is directly proportional to the rate of change of magnetic flux through the loop. In simpler terms, when the magnetic field passing through a conductor changes, it generates an electric current in the conductor.
7. Why does the negative sign appear in the mathematical expression of Faraday's Law?
The negative sign in Faraday's Law (ε = -dΦ/dt) represents Lenz's Law. It indicates that the induced EMF opposes the change in magnetic flux. This opposition is nature's way of conserving energy in electromagnetic systems.
8. How does changing magnetic flux induce a current?
Changing magnetic flux creates an electric field within the conductor. This electric field causes free electrons in the conductor to move, resulting in an induced current. The faster the change in magnetic flux, the stronger the induced current.
9. What factors affect the strength of the induced EMF?
The strength of the induced EMF depends on three main factors: the strength of the magnetic field, the area of the loop or coil, and the rate at which the magnetic field changes. Increasing any of these factors will increase the induced EMF.
10. Can a stationary magnet induce a current in a stationary wire?
No, a stationary magnet cannot induce a current in a stationary wire. There must be relative motion or a change in the magnetic field to induce a current. This is because Faraday's Law requires a change in magnetic flux to generate an EMF.
11. How does a transformer work based on Faraday's Law?
A transformer works on the principle of electromagnetic induction. It has two coils: primary and secondary. When an alternating current flows through the primary coil, it creates a changing magnetic field. This changing field induces a current in the secondary coil, effectively transferring electrical energy between the coils.
12. How does a generator convert mechanical energy into electrical energy?
A generator uses Faraday's Law to convert mechanical energy into electrical energy. It typically consists of a coil rotating in a magnetic field. As the coil rotates, the magnetic flux through it changes, inducing an EMF and thus generating electricity.
13. What is magnetic flux and why is it important in Faraday's Law?
Magnetic flux is a measure of the total magnetic field passing through a given area. It's calculated as the product of the magnetic field strength, the area, and the cosine of the angle between the field and the area's normal. It's crucial in Faraday's Law because the rate of change of magnetic flux determines the induced EMF.
14. Can Faraday's Law explain the working of an electric guitar pickup?
Yes, electric guitar pickups work based on Faraday's Law. The pickup consists of a magnet wrapped with a coil of wire. When a steel guitar string vibrates near the pickup, it causes variations in the magnetic field. These variations induce a current in the coil, which is then amplified to produce sound.
15. What is the difference between motional EMF and transformer EMF?
Motional EMF is induced when a conductor moves through a stationary magnetic field, while transformer EMF is induced when a stationary conductor experiences a changing magnetic field. Both are applications of Faraday's Law, but the source of flux change differs.
16. What is the significance of Faraday's ice pail experiment?
Faraday's ice pail experiment demonstrated that electric charge is induced on the surface of a conductor, not inside it. This led to the concept of electrostatic shielding and Faraday cages. While not directly related to electromagnetic induction, it was a crucial experiment in Faraday's exploration of electromagnetism.
17. What is the relationship between Faraday's Law and Maxwell's equations?
Faraday's Law is one of Maxwell's four fundamental equations of electromagnetism. Specifically, it's represented by Maxwell's third equation, which states that a changing magnetic field produces an electric field. This equation mathematically expresses Faraday's experimental observations.
18. How does Faraday's Law relate to the concept of electromagnetic waves?
Faraday's Law is a crucial component in understanding electromagnetic waves. It shows that a changing magnetic field creates an electric field. When combined with Ampère's Law (which shows that a changing electric field creates a magnetic field), it forms the basis for the propagation of electromagnetic waves, as described by Maxwell's equations.
19. What is the difference between Faraday's Law and the Lorentz Force Law?
While both laws deal with electromagnetic interactions, they describe different aspects. Faraday's Law explains how a changing magnetic field induces an EMF in a conductor. The Lorentz Force Law, on the other hand, describes the force experienced by a charged particle moving in an electromagnetic field. Both laws are fundamental to electromagnetism but apply to different scenarios.
20. What is Lenz's Law and how does it relate to Faraday's Law?
Lenz's Law is a consequence of Faraday's Law that states the direction of the induced current is such that it opposes the change in magnetic flux that caused it. It explains why the induced current creates a magnetic field that opposes the original change in magnetic flux.
21. How does Faraday's Law explain the operation of a betatron?
A betatron is a particle accelerator that uses Faraday's Law to accelerate electrons. It employs a changing magnetic field to induce a circular electric field, which accelerates electrons in a circular path. The changing magnetic flux induces an EMF that continuously accelerates the electrons to high energies.
22. What is the role of Faraday's Law in the Earth's magnetic field and auroras?
Faraday's Law helps explain the generation of Earth's magnetic field through the dynamo effect in the planet's liquid outer core. It also plays a role in auroras: when charged particles from the Sun interact with Earth's magnetic field, they induce electric currents in the upper atmosphere, creating the beautiful light displays.
23. How does Faraday's Law apply to superconductors?
In superconductors, Faraday's Law manifests uniquely. When a superconductor is exposed to a changing magnetic field, it induces persistent currents that exactly cancel the change in magnetic flux inside the superconductor. This perfect diamagnetism, known as the Meissner effect, is a consequence of Faraday's Law and superconductivity.
24. What is the difference between self-inductance and mutual inductance?
Self-inductance occurs when a changing current in a coil induces an EMF in the same coil, opposing the change in current. Mutual inductance, on the other hand, involves two separate coils where a changing current in one induces an EMF in the other. Both phenomena are based on Faraday's Law of Induction.
25. How does Faraday's Law explain the working of a metal detector?
Metal detectors use Faraday's Law by creating an alternating magnetic field from a coil. When this field encounters a metal object, it induces eddy currents in the metal. These currents create their own magnetic field, which is detected by the device. The strength and phase of this secondary field indicate the presence and properties of the metal.
26. Can Faraday's Law be applied to non-electrical systems?
While Faraday's Law is primarily associated with electromagnetic systems, its principle of induced effects due to changes can be analogously applied to other fields. For example, in fluid dynamics, the motion of a fluid can induce forces in nearby objects, similar to how changing magnetic fields induce currents in conductors.
27. What is the significance of Faraday's Law in modern technology?
Faraday's Law is fundamental to many modern technologies. It's crucial in the operation of electric motors, generators, transformers, and induction cooktops. It's also vital in the design of magnetic resonance imaging (MRI) machines, wireless charging systems, and in the development of renewable energy technologies like wind turbines and wave energy converters.
28. How does Faraday's Law explain the skin effect in conductors?
The skin effect, where alternating current tends to flow near the surface of a conductor, can be explained using Faraday's Law. The changing current creates a changing magnetic field inside the conductor, which induces opposing currents in the conductor's interior. This results in the current being concentrated near the surface, especially at high frequencies.
29. What is the role of Faraday's Law in wireless power transfer?
Wireless power transfer relies heavily on Faraday's Law. A changing current in a transmitting coil creates a changing magnetic field. This field induces a current in a receiving coil, effectively transferring power without physical contact. The efficiency of this transfer depends on factors like coil design and distance, all governed by Faraday's Law.
30. How does Faraday's Law explain the operation of a Hall effect sensor?
While the Hall effect itself is not a direct application of Faraday's Law, Hall effect sensors often use Faraday's Law in their operation. The changing magnetic field caused by the movement of a magnet near the sensor induces a current, which can be detected and measured. This principle is used in various applications, including speed sensors in vehicles.
31. What is the significance of Faraday's Law in geophysics?
In geophysics, Faraday's Law is crucial for understanding and measuring Earth's magnetic field variations. It's used in magnetotelluric surveys, where natural variations in the Earth's magnetic field induce electric currents in the ground. By measuring these induced currents, geophysicists can infer the electrical properties of subsurface structures.
32. What is the relationship between Faraday's Law and Lenz's Law in superconductors?
In superconductors, the interplay between Faraday's Law and Lenz's Law leads to unique behavior. When a superconductor is exposed to a changing magnetic field, Faraday's Law induces currents. These currents, according to Lenz's Law, create a magnetic field that exactly cancels the external field change inside the superconductor, resulting in perfect diamagnetism (the Meissner effect).
33. How does Faraday's Law apply to the concept of motional EMF in space physics?
In space physics, motional EMF occurs when a conductor (like a spacecraft or a planet's ionosphere) moves through a magnetic field (such as the interplanetary magnetic field). According to Faraday's Law, this motion induces an electric field and potential difference across the conductor. This principle is important in understanding phenomena like the electrodynamics of planetary magnetospheres.
34. What is the role of Faraday's Law in understanding magnetic reconnection?
Magnetic reconnection, a process where magnetic field lines break and reconnect, releasing energy, can be partially understood through Faraday's Law. The rapid change in magnetic field topology during reconnection induces strong electric fields according to Faraday's Law. These induced fields play a crucial role in particle acceleration and energy release in phenomena like solar flares and magnetospheric substorms.
35. How does Faraday's Law explain the operation of a flux gate magnetometer?
A flux gate magnetometer uses Faraday's Law to measure magnetic fields. It contains a core of easily magnetized material surrounded by two coils. An alternating current in one coil saturates the core, and the external magnetic field to be measured causes asymmetry in this saturation. This asymmetry induces a current in the second coil, which is proportional to the external field strength.
36. What is the significance of Faraday's Law in the development of electromagnetic launchers?
Electromagnetic launchers, such as railguns and coilguns, rely on Faraday's Law. In a coilgun, for example, a series of electromagnetic coils are energized sequentially to create a moving magnetic field. This changing field induces currents in the projectile or in a conductive sabot, propelling it forward at high speeds.
37. How does Faraday's Law apply to the concept of magnetic levitation?
Magnetic levitation (maglev) technology often uses principles derived from Faraday's Law. In electrodynamic suspension systems, for instance, the movement of superconducting coils over conducting plates induces eddy currents. These currents create a magnetic field that opposes the motion, providing a levitation force. The strength of this effect depends on the rate of change of magnetic flux, as described by Faraday's Law.
38. How does Faraday's Law apply to eddy currents?
Eddy currents are circular electric currents induced within conductors by a changing magnetic field. According to Faraday's Law, these currents are generated to oppose the change in magnetic flux. Eddy currents can cause heating in conductors and are used in applications like induction cooking and electromagnetic braking.
39. How does the concept of mutual inductance relate to Faraday's Law?
Mutual inductance is a direct application of Faraday's Law involving two or more coils. When current changes in one coil, it creates a changing magnetic field that induces an EMF in nearby coils. The degree of this effect is measured by the mutual inductance, which depends on the coils' geometries and relative positions.
40. Why doesn't a DC current in a straight wire induce a current in a nearby loop?
A steady DC current produces a constant magnetic field, which doesn't change over time. Faraday's Law requires a change in magnetic flux to induce an EMF. Since there's no change in flux with a constant DC current, no EMF is induced in the nearby loop.
41. How does the orientation of a coil affect the induced EMF?
The orientation of a coil relative to the magnetic field affects the amount of magnetic flux passing through it. When the coil's plane is perpendicular to the field lines, maximum flux passes through, resulting in maximum induced EMF. As the angle changes, the flux and induced EMF decrease, becoming zero when the coil is parallel to the field.
42. What is magnetic damping and how does it relate to Faraday's Law?
Magnetic damping is the slowing of a moving conductor in a magnetic field due to induced currents. As the conductor moves, it experiences a changing magnetic flux, inducing eddy currents according to Faraday's Law. These currents create a magnetic field that opposes the motion, resulting in a damping effect.
43. How does the shape of a coil affect the induced EMF?
The shape of a coil affects the induced EMF by influencing the rate of change of magnetic flux. A tightly wound coil with many turns will experience a greater change in flux for a given change in magnetic field, resulting in a larger induced EMF. The cross-sectional area and orientation of the coil also play crucial roles.
44. What is electromagnetic braking and how does it use Faraday's Law?
Electromagnetic braking uses Faraday's Law to slow down moving objects. When a conductor moves through a magnetic field, it experiences an induced current. This current creates a magnetic field that opposes the motion, causing a braking effect. This principle is used in roller coasters, trains, and some types of exercise equipment.
45. What is the relationship between Faraday's Law and conservation of energy?
Faraday's Law is consistent with the principle of conservation of energy. The energy of the induced current comes from the work done to change the magnetic flux. In a generator, mechanical energy is converted to electrical energy. In a transformer, energy is transferred between coils. The negative sign in Faraday's Law ensures that energy is conserved in these processes.
46. How does Faraday's Law apply to the concept of inductance?
Inductance is a direct consequence of Faraday's Law. It represents a circuit's tendency to oppose changes in current flow. When current changes in a circuit, it creates a changing magnetic field, which in turn induces an EMF that opposes the change in current. This self-induced EMF is characterized by the circuit's inductance.
47. How does Faraday's Law relate to the concept of flux linkage?
Flux linkage is a key concept in understanding Faraday's Law. It's defined as the total magnetic flux passing through all turns of a coil. The rate of change of flux linkage determines the induced EMF according to Faraday's Law. This concept is particularly important in analyzing transformers and other multi-turn coil systems.
48. How does Faraday's Law explain the operation of a Faraday flashlight?
A Faraday flashlight, also known as a shake flashlight, uses Faraday's Law to generate electricity. It contains a magnet that moves through a coil when the flashlight is shaken. This changing magnetic flux induces a current in the coil, which is then used to charge a capacitor or battery to power the LED light.

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