Faraday's Law of Electromagnetic Induction

Faraday's Law Overview

Faraday's law of induction, in physics, is a quantitative connection indicating that a changing magnetic field generates a voltage in a circuit, discovered in 1831 by the English scientist Michael Faraday on the basis of experimental data. Faraday's law of electromagnetic induction, usually known as Faraday's law, is a fundamental rule of electromagnetism that explains how a magnetic field interacts with an electric circuit to create an electromotive force (EMF). This is referred to as electromagnetic induction. To uncover the phenomenon of electromagnetic induction, he conducted three major experiments.

Faraday's Law

Faraday's law of induction (abbreviated Faraday's law) is an electromagnetism fundamental law that predicts how a magnetic field would interact with an electric circuit to create an electromotive force (emf)—a phenomenon known as electromagnetic induction. It is the basic concept of transformers, inductors, and many other electrical motors, generators, and solenoids. The Maxwell-Faraday equation (listed as one of Maxwell's equations) states that a spatially varying (and possibly time-varying, depending on how a magnetic field varies in time) electric field always accompanies a time-varying magnetic field, whereas Faraday's law states that there is emf (electromotive force, defined as electromagnetic work done on a unit charge after it has traveled one round of a conductive loop). 

Faraday's law may be deduced from the Maxwell-Faraday equation (which describes transformer emf) and the Lorentz force (describing motional emf). The integral version of the Maxwell-Faraday equation only represents the transformer emf, whereas Faraday's law equation describes both the transformer and motional emf.

Also read more about- Magnetic Effect of Electric Current and Eddy Current.

Faraday's Law Examples

The following are some examples of Faraday's Law of Electromagnetic Induction-

1. A magnet is rapidly dragged toward a wire loop.
2. In the downward direction, the flux through the wire loop increases.
3. In the loop, a current begins to flow in the direction indicated by the arrow.
4. This current generates a magnetic field that points upward and resists the flux fluctuations that cause it.
5. The magnetic force generated by the magnet's loop serves to slow down the approaching magnet.

Faraday's First Law of Electromagnetic Induction

Faraday and Henry conducted a long series of experiments that led to the discovery and understanding of electromagnetic induction. Faraday deduced from his experimental findings that an emf is produced when the magnetic flux across the coil varies over time. 

Also read more about the Difference between Real and Virtual Images.

Faraday's first law of electromagnetic induction states-

An electromotive force is produced whenever a conductor is put in a changing magnetic field. When the conductor circuit is closed, a current, known as induced current, is induced. Any change in the magnetic field of a wire coil will produce an emf in the coil. This induced emf is known as induced emf, and if the conductor circuit is closed, current will circulate through the circuit as well, and this current is known as induced current.

Also read more about the Resistance Formula. 

Methods for Modifying the Magnetic Field

The following are some of the methods for modifying the magnetic field- 

1. By pushing a magnet closer or farther away from coil
2. By introducing or removing the coil from the magnetic field
3. By varying the area of a coil in a magnetic field
4. By rotating the coil with respect to the magnet

Faraday's Second Law of Electromagnetic Induction

It indicates that the magnitude of the induced emf in the coil equals the rate of change of the flux that links with the coil. The coil's flux linkage is the product of the number of turns in the coil and the flux associated with the coil. Faraday's law is expressed as follows-

where E is the electromotive force, N is the number of rotations, and t is the magnetic flux.

Also read more about the Refractive Index Formula and EMF Equation of DC Generator.

How to Boost the EMF Induced by a Coil

The following are some of the ways to boost induced EMF by a coil-

1. By increasing the number of turns in the coil, i.e. N, it is clear from the formulas obtained above that increasing the number of turns in a coil increases the induced emf.
2. By increasing the magnetic field strength, i.e. B around the coil- Mathematically, as the magnetic field grows, so does the flux, and as the flux increases, so does the induced emf. In theory, if the coil is passed through a greater magnetic field, there will be more lines of force for the coil to cut, resulting in more emf.
3. By raising the relative speed of the coil and the magnet - If the relative speed of the coil and the magnet is increased from its previous value, the coil will cut the lines of flux at a quicker rate, resulting in more induced emf.

Also read more about the Father of Physics and Faraday Constant.

Faraday's Law Derivation

Consider a magnet coming up to a coil. Consider the following two-time instances- T₁and T₂.

NΦ₁represents the flux connection with the coil at moment T₁.

NΦ₂represents the flux connection with the coil at moment T₂.

The flux linkage changes as a result of, 

N(Φ₂– Φ₁)

Consider this shift in flux connection as,

Φ = Φ₂– Φ₁

As a result, the flux linkage change is given by NΦ.

The flux linkage rate of change is given by NΦ/t.

Taking the derivative of the above equation, we obtain, N dΦ/dt

The induced emf in a coil is equal to the rate of change of the flux linkage, according to Faraday's second law of electromagnetic induction. Therefore,

Considering Lenz's law,

The following details are deduced from the preceding equation-

1. The induced emf grows as the number of turns in the coil increases.
2. The induced emf grows as the magnetic field intensity increases.
3. The higher emf is caused by increasing the speed of the relative motion between the coil and the magnet.

Also read more about the Law of Variable Proportion.

Faraday's Law Experiment Relationship Between Induced EMF and Flux

1. In the first experiment, he demonstrated that current is only produced when the intensity of the magnetic field is altered. An ammeter was linked to a loop of wire, and when a magnet was pulled toward the wire, the ammeter deflected.
2. In the second experiment, he demonstrated that putting a current through an iron rod causes it to become electromagnetic. He discovered that when there is a relative motion between the magnet and the coil, an electromotive force is created. No electromotive force was noticed while the magnet was maintained fixed around its axis, but the induced electromotive force was created when the magnet was rotated about its own axis. When the magnet was held steady, the ammeter showed no deflection.
3. During the third experiment, he observed that the galvanometer did not deflect and that no induced current was created in the coil when it was held away from a stationary magnetic field. When the magnet was removed from the loop, the ammeter deflected in the other direction.

The following gives information about the link between the location of the magnet and the deflection in the Galvanometer by summarising the above points in a table- 

Also read more about the Electrical Power Formula. 

Applications of Faraday's Law

Faraday's law has applications in the following fields-

1. Faraday's law governs the operation of electrical devices like transformers.
2. Induction cookers operate on the idea of reciprocal induction, which is based on Faraday's law.
3. The velocity of the fluids is measured by applying an electromotive force to an electromagnetic flowmeter.
4. Electric guitars and electric violins are examples of musical instruments that use Faraday's law.
5. Maxwell's equation is based on Faraday's principles, which indicate that a change in the magnetic field causes a change in the electric field.

Also read more about the SI Unit of Electric Flux. 

Conclusion

Faraday eventually established that if there was relative motion between a conductor and a magnetic field, the flux connection with a coil changed, and this change in flux created a voltage across a coil. Faraday's law states that "the electromotive force is created when the magnetic flux or magnetic field varies with time." In addition, based on the foregoing tests, Michael Faraday developed two laws.