Before introducing Faraday’s laws, it is necessary to understand magnetic flux and its formula. 

Magnetic flux is the measurement of the total magnetic field that passes through a given area. Its formula is

ΦB = Magnetic field * Area of given surface= BA cos θ,

where B is the magnitude of the magnetic field, the area of the given surface is A, and the angle between B and A is θ. Magnetic flux has the SI unit weber (Wb) or tesla meter squared (T m2). 

Here it is imperative to remember Gauss’s Law of Magnetism, which states that the total flux of the magnetic field is zero outside of the given surface.

Through experiments, Faraday concluded that when magnetic flux through a coil changes with time, an electromotive force (emf) gets induced in the coil. He made observations from these experiments in the form of a law called Faraday’s law of electromagnetic induction. It states that the magnitude of the induced emf in a circuit is equal to the rate of change of magnetic flux through the circuit with respect to time. The Faraday’s law formula is represented as,

ε = − dΦBdt

where ε is the induced emf, and the magnetic flux is ΦB. This is also called the magnetic induction formula.

The negative sign indicates the direction of the ε and hence the direction of the current in the closed-loop. If the coil is closely wound with N turns, the change of flux associated with each turn is the same. Thus, the total induced emf is

ε = −N dΦBdt

This means that the emf can be increased by increasing the number of turns N of the coil.

On observation, we will notice that the 19th century is a milestone in the field of physics. Several discoveries were made, and many laws were formulated. For example, in 1834 we had physicist Heinrich Fredrich Lenz who deduced a law called Lenz’s law based on the induced emf polarity. The law states that the induced emf has such a polarity that it produces a current that opposes a change in the magnetic flux that created it. This is represented by the negative sign in the formula for induced emf.

We have studied that induced currents flow in well-defined paths in conductors such as circular loops. The shape of these loops resembles eddies in the water. To see these, you will have to go to an oceanside and that too in an aeroplane and fly low. Physicist Foucault discovered this effect.

By Lenz’s law, an eddy current creates a magnetic field that opposes the change in the magnetic field that created it. This makes it undesirable, as it heats the core and dissipates electrical energy in the form of heat.

Applications: The opposing nature of eddy currents is useful in specific applications like magnetic braking in trains, electromagnetic damping, induction furnace, electric power meters, etc.

It was observed that an electric current is induced in a coil if there is a flux change in another coil nearby or within the same coil. This is called inductance. Here, the magnetic flux through a coil is directly proportional to the current induced.

That is ΦB α I. And if the geometry of the coil does not change with time, then, dΦBdtα dIdt . For a coil with N turns, N ΦB α I.

Mutual Inductance: If there are two solenoids S1 and S2, with turns N1 and N2 respectively, and a current I2 is set up through S2, then the corresponding flux linkage in S1 can be denoted by

N1 Φ1 = M12 I2

where the constant of proportionality M12, is the mutual inductance of solenoid S1 with respect to solenoid S2 and is also called the coefficient of mutual induction. Its SI unit is Henry (H).

Self-Inductance: It is the phenomenon where emf is induced in a coil due to a change of flux through it by varying the current through itself. 

Here, N ΦB α I and N ΦB = L I, 

where L is the constant of proportionality and self-inductance of the coil, and it is named the coefficient of self-induction of the coil. Its SI unit is also Henry (H).

As mentioned above, there are numerous applications of Faraday’s laws, of which generating alternating currents is one of the most important. It is even suggested that the migratory patterns of birds must be due to the electromagnetic induction created by the earth’s magnetic field. 

Think about it – the Arctic tern, an elegant white sea bird, migrates some 40,000 km every year, and the beautiful pink flamingos migrate from Iran and Pakistan to Mumbai. Is electromagnetic induction involved in this? Find the answer on www.msvgo.com.