Overview of the Faraday’s Law of Induction

• Faraday’s induction law indicates how electromotive force (emf) is generated when a magnetic field interacts with an electric current. The phenomenon through which the electromotive force (emf) is produced is called electromagnetic induction. It is the basic underlying principle by which many electrical motors, inductors, generators, transformers, and solenoids operate. 

• Electromagnetic induction was observed separately by Michael Faraday in 1831 and Joseph Henry in 1832. However, Michael Faraday was the first to publish the results of his experiments, and hence, the induction laws are named after him.

• Michael Faraday postulated two electromagnetic induction laws. The first law explains how an emf is induced in a conductor when it is kept in a changing magnetic field, while the second determines the strength of the emf produced in the conductor. 

• While Christian Ørsted discovered that magnetic fields are produced by the electrical current before Faraday, James Clark Maxwell used Faraday’s induction laws in his equations to describe the relationship between electricity and magnetism, merging them into a single electromagnetic force.

Electromagnetic Induction

• Faraday discovered that whenever the magnetic flux passing through a circuit changes, an electromotive force is produced in the circuit.

• A current flows through the circuit if it is closed. The emf and current generated are called induced emf and induced current, respectively, and last only while the magnetic flux is changing. This is called electromagnetic induction. 

• The magnetic field in a circuit can be changed in the following ways:

1. By moving a magnet with respect to the circuit
2. By changing the current in a neighbouring circuit
3. By changing the current within the circuit
4. When a coil is rotated in the magnetic field

Electromotive force

Electromotive force is the potential difference generated in a circuit by a battery or a variation in the magnetic field. It is represented by ε and is measured in volts. 

What is Faraday’s law?

Faraday came up with two induction laws to explain how electromotive force (emf) is generated when a magnetic field interacts with an electric current. 

Faraday’s First Law of Induction

• Faraday’s first induction law states that any variation in the magnetic flux in a circuit results in the induction of an electromotive force in the circuit.
• This electromotive force is known as induced emf, and an induced current will flow through the circuit if it is closed. 
• If ΔΦis the magnetic flux in a time interval Δt, then the emf induced in the circuit is given by: ε=-ΔΦ Δt
• At the limit Δt0, ε=-dΦ dt

If dΦ is in ‘weber’ and dt is in second, then the induced emf ε will be in volt. 

Faraday’s Second Law of Induction

• Faraday’s second electromagnetic induction law proposes that the strength of the induced emf in a coil is equivalent to the rate of variation of magnetic flux. 
• The emf generated is dependent on the number of turns in the coil and the magnetic flux related to the coil. The emf is induced for every turn of the coil and the emf of every turn is added up. 
• Therefore, for a coil of N turns and a magnetic flux dΦ in a time interval dt, the emf will be:

ε=-NdΦ dt = –d(NΦ) dt

Lenz’s Law

• Lenz’s induction law denotes that the direction of the induced emf, or the current in any circuit, is such that it tends to oppose the change in magnetic flux that produced it.
• This is the cause of the negative sign in the equation. The negative sign indicates that the direction of the magnetic field and the direction of the induced emf are opposite to each other. It is important for maintaining the structure of Faraday’s law.

How is Faraday’s Law derived?

Consider a Faraday’s law experiment in which a magnet is approaching a coil. 

Considering the magnetic flux linkages at two time intervals, T1 and T2:

• Magnetic flux linkage in the coil at the time T1 is 

T1 = NΦ1

• Magnetic flux linkage in the coil at the time T2 is

T2 =NΦ2

• Change in magnetic flux linkage becomes 

N(Φ2–Φ1)

• This change in magnetic flux linkage can be represented as

Φ = (Φ2–Φ1)

• Therefore, the change in magnetic flux linkages becomes

NΦ

• The rate of change in the magnetic flux linkage is NΦ/t
• Differentiating the above equation, we get 

NdΦdt

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

ε=NdΦdt

• Considering Lenz’s law,

ε= -NdΦdt

Where, 

Magnetic flux Φ= B.A

B = Strength of the magnetic field

A = area of the coil within the magnetic field

Factors affecting the electromotive force

• Number of turns in the coil

Since the emf is a product of the number of turns (N) and the rate of change of magnetic flux, the magnitude of the emf produced is directly proportional to the number of turns in the coil.

• Strength of the Magnetic field 

The magnetic flux within a coil increases with the increase in the strength of the magnetic field. With an increase in magnetic flux, the induced emf will also increase.

• Area of the coil within the magnetic field

The induced emf varies proportionally with the area of the coil within the magnetic field. If the area of the coil within the magnetic field increases, the induced emf will also increase.

Conclusion

• Faraday’s discoveries and induction laws have made a significant impact on our understanding of electromagnetic induction. He explains through his two induction laws that a magnetic field within a coil in a circuit produces an induced electromotive force and an induced current. He also states that the magnitude of this induced emf is equal to the rate of change of magnetic flux and the number of turns of the coil.
• Lenz’s law determines the direction of the induced emf or current. It is such that it opposes the change in magnetic flux that produced it. 
• We also see that the induced emf is a factor of the number of turns in the coil, magnetic strength, and the area of the coil in the magnetic field.