Faraday’s Laws of Electromagnetic Induction

Faraday’s law of electromagnetic induction shows the relationship between magnetic field, electric current, and an electromotive force(EMF).

In nature, there are two mutually dependent phenomena namely electricity and magnetism. Electromagnetism is the branch of physics that deals with the study of the effects of electricity and magnetism, and their dependence on each other.

At present, it is a well-known fact that a changing magnetic field can produce an EMF (Electromotive Force) and a moving charge (or electric current) can produce a magnetic field. However, these concepts are the results of several experiments performed by many physicists and engineers.

One of them is Michael Faraday who developed two basic laws of electromagnetic induction in 1831. These laws are popularly known as Faraday’s First Law and Faraday’s Second Law of Electromagnetic Induction. These two laws explain how a changing magnetic field produces an EMF in a moving conductor.

What is Electromagnetic Induction?

When there is a change in the magnetic field linked to a conductor, an electromotive force (EMF) is induced in the conductor, this phenomenon is known as electromagnetic induction. Electromagnetic induction is the most fundamental principle on which today’s many electrical devices such as motors, generators, measuring instruments, etc. work.

Faraday’s Law of Electromagnetic Induction

Faraday’s first law of electromagnetic induction describes the induction of electromotive force in a conductor and Faraday’s second law gives the magnitude of electromotive force induced in the conductor.

Two physicists Michael Faraday and Joseph Henry performed a long series of experiments. From the observations of these experiments, Faraday described that when a changing magnetic field links to a conductor, an emf is induced in the conductor.

Faraday’s First Law

Faraday’s first law of electromagnetic induction states that Whenever a magnetic field linked to a conductor changes, an electromotive force (emf) is induced in the conductor.”

If the conductor circuit is closed, a current, called induced current, starts flowing through the conductor.

The change in the magnetic field linked to the conductor can be brought in two ways as follows:

  • By moving the conductor relative to the stationary magnetic field.
  • By moving the magnetic field while the conductor is held stationary.

Faraday’s Second Law

Faraday’s second law states that “the magnitude of the induced emf in the conductor is equal to the rate of change of magnetic flux linked to the conductor.”

Derivation of Faraday’s Law

Faraday’s Laws of Electromagnetic Induction

Consider a coil having N conductors and a magnetic is moving towards the coil, then

At the initial position, the flux linkage with the coil is

initial flux linkage with the coil

At the final condition, the flux linkage with the coil is

final flux linkage with the coil
Hence, the change in the flux linkage is,
change in flux

Now, the rate of change of this flux linkage is

rate of change of  flux linkage as per faraday law

According to Faraday’s second law of electromagnetic induction, the EMF induced in the conductor is equal to the rate of change of flux linkage.

faraday law equation

In differential form,

faraday law equation in differential form

Where, 𝜙 =𝜙2-𝜙1, the total change in magnetic flux.

Applications of Faraday’s Laws of Electromagnetic Induction

Faraday’s laws are the most fundamental law in electromagnetism. These laws are widely used in many areas of electrical engineering like electrical machines, measuring instruments, in medicine for diagnosis of disease, etc. Some common applications of Faraday’s laws are:

  • The transformer operates on the principle of electromagnetic induction. Therefore, Faraday’s law can be for its analysis.
  • The production of electricity by a generator is also based on Faraday’s laws of electromagnetic induction.
  • Faraday’s laws are also the basis of the operation of many other appliances such as induction cookers, electromagnetic flow meters, electric guitars, electric violins, etc.

Solved Problems on Faraday’s Laws of Electromagnetic Induction

A coil that has 700 turns develops an average induced voltage of 50 V. What must be the change in the magnetic flux occur to produce such a voltage if the time interval for this change is 0.7 seconds.

Given Data:

Now, by Faraday’s law, we get,

solved problem on faraday's law of electromagnetic induction

The magnetic flux linked with a coil having 250 turns is changed from 1.4 Wb to 2 Wb in 0.45 seconds. Calculate the induced emf in the coil.

Given data,

Now, according to Faraday’s law, we have,

numerical problem on faraday's law of electromagnetic induction
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