Induced EMF: The generation of the electromotive force in a coil due to the change in magnetic flux linked with the coil is termed an induced emf. The generation of the induced emf is based on Faraday’s Law of Electromagnetic Induction.

Induced emf is an important concept in electricity and electronics, as it plays a key role in the generation and transmission of electrical power. It is also used in a variety of applications, including electric motors, generators, and transformers, which are all essential components of our modern electrical infrastructure.

This section of the post will be focused on the induced emf, and how can the emf be generated (statically induced emf and dynamically induced emf). Also, insight will be given into Lenz’s law.

Contents

## Mathematical Expression of Induced EMF

Let us consider a coil with N number of turns. The flux linking the coil is changed by dΦ amount in dt interval.

Now, according to Faraday’s Law of Electromagnetic Induction,
EMF induced in the coil,
e = Rate of change of flux linked with the coil
=Number of turns (N) x rate of change of flux (dΦ/dt)
=N
x dΦ/dt

The emf induced in the coil ‘E’ is given by
e= –N * dΦ/dt

The negative sign in the emf relation is due to the Lenz law.

## Lenz Law

The direction of the induced current in a circuit as a result of a change in the magnetic field around the circuit is described by Lenz’s law. According to Lenz’s law, the induced current will always operate to counteract the change in the magnetic field that it created.

Mathematically, Lenz’s law can be expressed as:

E= -N * dΦ/dt

Where F is the induced electromotive force, N is the number of turns in the circuit, and dΦ/dt is the rate of change of the magnetic flux through the circuit. The negative sign indicates that the induced current will always act to oppose the change in the magnetic field.

For example, think of a basic circuit that consists of a single coil of wire with a bar magnet inserted within. The magnetic field surrounding the coil will increase if the bar magnet is traveling in the direction of the coil. Lenz’s law states that this will result in an induced current flowing in the coil in a manner that opposes the rise in the magnetic field brought on by the moving bar magnet. The bar magnet’s motion will be slowed down as a result of this force.

## Statically and Dynamically Induced EMF

The electric potential difference created between two conductor ends when the magnetic field around the wire changes is known as the statically induced electromotive force (EMF). This phenomenon is termed electromagnetic induction.

This is explained in the above section with the equation, e= –N * dΦ/dt.

An electrical current can be produced in a circuit using the statically generated EMF. For instance, the statically generated EMF will cause a current to flow in a conductor if it is put in a magnetic field that is changing. Electrical equipment can be powered by this current, or work can be done.

The electric potential difference created between two conductor ends as the conductor travels through a magnetic field is known as the dynamically induced electromotive force (EMF).

According to Faraday’s law of electromagnetic induction, the dynamically generated EMF in a conductor is given by:

e = -Blv

Where ε is the dynamically generated EMF, B is the strength of the magnetic field, l is the length of the conductor, and v is the velocity of the conductor. The negative sign shows that, according to Lenz’s law, the direction of the induced current will always be such that it opposes the change in the magnetic field that created it.

## Conclusion

In conclusion, an electrical conductor experiences an induced emf as it moves through a magnetic field or when the magnetic field around it is altered. It is a crucial idea in electricity and electronics and has many applications, such as the production and transfer of electrical power.