# Faraday’s Law of Electromagnetic Induction

Faraday’s law of electromagnetic induction, also known as Faraday’s law, is the basic law of electromagnetism which helps us to predict how a magnetic field would interact with an electric circuit to produce an electromotive force (EMF). This phenomenon is known as electromagnetic induction.

Michael Faraday proposed the laws of electromagnetic induction in the year 1831. Faraday’s law or the law of electromagnetic induction is the observation or results of the experiments conducted by Faraday. However, he performed three main experiments to discover the phenomenon of electromagnetic induction.

## History

Electromagnetic induction was discovered independently by Michael Faraday in 1831 and Joseph Henry in 1832. Faraday was the first to publish the results of his experiments.

In Faraday’s first experimental demonstration of electromagnetic induction (August 29, 1831). He wrapped two wires around opposite sides of an iron ring (torus) (an arrangement similar to a modern toroidal transformer).

Based on his assessment of recently discovered properties of electromagnets, he expected that when current started to flow in one wire, a sort of wave would travel through the ring and cause some electrical effect on the opposite side.

He plugged one wire into a galvanometer and watched it as he connected the other wire to a battery. Indeed, he saw a transient current (which he called a “wave of electricity”) when he connected the wire to the battery and another when he disconnected it.:182–183​ This induction was due to the change in magnetic flux that occurred when the battery was connected and disconnected.

Within two months, Faraday had found several other manifestations of electromagnetic induction.

## Faraday’s First Law Of Electromagnetic Induction

Therefore, Faraday’s first law of electromagnetic induction states that whenever a conductor is placed in a varying magnetic field, an electromotive force is induced. If the conductor circuit is closed, a current is induced, which is called induced current.

## Faraday’s Second Law of Electromagnetic Induction

Faraday’s second law of electromagnetic induction states that: The induced emf in a coil is equal to the rate of change of flux linkage.

The flux is the product of the number of turns in the coil and the flux associated with the coil. The formula of Faraday’s law is given below:

ε=−N x Δϕ/Δt

Where ε is the electromotive force, Φ is the magnetic flux, and N is the number of turns.

Consider a magnet approaching towards a coil. Consider two-time instances T1 and T2

Flux linkage with the coil at the time T1 is given by

T1 = NΦ1

Flux linkage with the coil at the time T2 is given by

T2 = NΦ2

Change in the flux linkage is given by

N(Φ2 – Φ1)

Let us consider this change in flux linkage as

Φ = Φ2 – Φ1

Hence, the change in flux linkage is given by

Therefore, The rate of change of flux linkage is given by

NΦ/t

Taking the derivative of the above equation, we get

N dΦ/dt

According to Faraday’s second law of electromagnetic induction, we know that the induced emf in a coil is equal to the rate of change of flux linkage. Therefore,

E=N x dϕ/dt

Considering Lenz’s law,

E=−Nx dϕ/dt

From the above equation, we can conclude the following

• Increase in the number of turns in the coil increases the induced emf
• Increasing the magnetic field strength increases the induced emf
• Also increasing the speed of the relative motion between the coil and the magnet results in the increased emf

Following are the applications of Faraday’s law:

1. The electrical equipment like transformers works on the basis of Faraday’s law.

2. Also the induction cooker works on the basis of mutual induction, which is the principle of Faraday’s law.

3. By inducing an electromotive force into an electromagnetic flowmeter, the velocity of the fluids is recorded.

4. Electric guitar and electric violin are musical instruments that find an application of Faraday’s law.

5. However, Maxwell’s equation is based on the converse of Faraday’s laws which states that change in the magnetic field brings a change in the electric field.

## Limitation of Faraday’s Law of Electromagnetic Induction

A major drawback to this version of Faraday’s law is that it is true only for an infinitely long loop of closed wire.