Electromagnetic Induction

# Faraday’s Laws of Electromagnetic Induction

## Electromagnetic Induction

In 1820, Oersted discovered the magnetic effect of current i.e. magnetic field exists around a current carrying conductor. In other words, magnetic field can be produced by means of an electric current. In 1831, British physicist Michael Faraday and American physicist Joseph Henry showed that the reverse effect to the magnetic field is also possible i.e. an electric current can be generated by means of magnetic field. Faraday demonstrated that when the magnetic flux linking a conductor changes, an emf is induced in the conductor. He gave the name of this phenomenon as electromagnetic induction.

The phenomenon in which an emf is induced in a coil or conductor due to the change in magnetic flux linked with the coil or conductor is called electromagnetic induction. The emf thus produced is known as induced emf and the current that flows through the coil is known as induced current.

Two things can be noted here, first, the basic requirement for electromagnetic induction is the change in the magnetic flux linking the coil or conductor. Secondly, the emf and hence current in the coil or conductor persist so long as this change is taking place.

A stationary charge produces only electric field while a moving charge produces both electric and magnetic field. The current is due to the motion of charged particles so the current or moving charge becomes the source of magnetism.

The magnitude of the induced emf in a coil or conductor due to electromagnetic induction can be determined by Faraday’s laws whereas the direction of induced emf can be determined by either Lenz’s law or Fleming left hand rule.

## Faraday’s Laws of Electromagnetic Induction

Faraday performed a series of experiments and collected the results of these experiments. Based on the results, he summed up his conclusions, known as Faraday’s laws of electromagnetic induction which are given below:

1. When the magnetic flux linking a coil or a conductor changes, an emf is induced in it.
2. The induced emf lasts so long as the change in magnetic flux is taking place.
3. The magnitude of induced emf is directly proportional to the rate of change of flux linkage.

Let the magnetic flux linking a coil changes from $\phi_1$ to $\phi_2$ in time $t$. Then, an emf $\varepsilon$ is induced in the coil. According to Faraday’s laws of electromagnetic induction, $\text{Induced emf}∝\text{Rate of change of flux linkage}$ $\text{i.e.}\varepsilon ∝-\frac{\phi_2-\phi_1}{t}$ $\varepsilon=-k\frac{\phi_2-\phi_1}{t}$

where, $k$ is a proportionality constant. In SI units, $k=1$. The negative sign in the equation is due to Lenz’s law i.e. the induced emf is in such a direction to oppose the cause due to which it is produced.

$\therefore\varepsilon=-\frac{\phi_2-\phi_1}{t}$

In differential form, $\varepsilon=-\frac{d\phi}{dt}$

For $N$ number of turns in the coil, $\varepsilon=-N\frac{d\phi}{dt}$

This gives the magnitude of the emf induced due to electromagnetic induction.

Next: Lenz’s Law