How Mutual Inductance functions and Learn About its Related Law

An electric current can be induced in a coil by flux change produced by another coil in its proximity or flux change produced by the same coil. In both cases, the flux through the coil is proportional to the current.

That is, Ø_B ∝ I

For a closely looped coil of N turns, the same magnetic flux is linked with all the turns. When the flux ∅_B through the coil changes, each turn contributes to the generated electromotive force. This is described using the term flux linkage which is equal to N∅_B for a closely wound coil. In such a case,

NØ_B ∝ I

The constant of proportionality in this context is called inductance. It is affected by the shape of the coil and core material properties. It is a scalar quantity.

Henry is the SI unit of inductance. It is denoted by H. It is named after Joseph Henry, an eminent physicist who discovered electromagnetic induction in the USA, independently of Faraday in England.

Mutual Inductance

When an electric current is induced in a coil due to flux change in the coil’s proximity, it is called mutual inductance. In simple words, when a voltage change in one coil induces a voltage in another coil near it, it is known as mutual inductance. The formula for mutual inductance is as follows:

Here,

N₁ = Turns of coil 1

N₂ = Turns of coil 2

A = Cross-sectional area in m²

L= Length of the coil in metres

μ₀ = Permeability of free space= 4𝜋*10^-7

μ_r = Relative permeability of the soft iron core

The distance between the coils and the shape of the coils affects the mutual inductance of two coils, solenoids, etc.

Functioning

Let’s take two lengthy coaxial solenoids each of length l.
Denote the radius of the inner solenoid S₁ by r₁ and the number of turns per unit let by n₁. The outer solenoid will be denoted by S₂, r₂, and n₂. Let N₁ and N₂ be the total numbers of turns of coils S₁and S₂, respectively.
When a current I₂ is set up through S₂, it, in turn, sets up magnetic flux through S₁, denoted by ∅₁. Now, the corresponding flux linkage with solenoid S₁ is

N₁∅₁=M₁₂I₂

The mutual inductance of solenoid S₁ with respect to solenoid S₂ is known as M₁₂. It can also be known as the coefficient of mutual induction.

Functions

The functions of mutual inductance in physics are as follows:

All the electric equipment that requires a magnetic field uses mutual induction.
It is also used in electric motors.
The mutual inductance of a transformer is called the coefficient of coupling. It is the measurement of the efficiency of power transfer from primary coils to secondary coils.
It is the property of a coil that is responsible for influencing or modifying the current and voltage in the secondary coil.
One of the functions of mutual induction is the formation of eddy current and generation in the test material.

Factors that Affect Mutual Inductance

The cross-sectional area of the coil.
The number of turns made by the coil.
The angle of the turns made by the coil.
The space between the two coils.
It is also affected by the medium of permeability between the two coils.

Features

It is a form of electromagnetic induction.
It was initially explained by Joseph Henry.
Two coils or wires or solenoids etc., are used, and a change in the flow of the current of one coil results in the generation of electromotive force in another.
Its main disadvantage is that the inductance from one coil to another can disrupt the functioning of the main coil.
The position of the coils decides the amount of inductance that takes place.
It can be increased by placing them on a soft iron core.
It can also be increased by decreasing the distance between the two coils or by increasing the number of turns of the coils.

Distinction Between Mutual Inductance and Self-Inductance

Mutual-Inductance	Self-Inductance
When voltage changes in one coil induce a voltage in another coil, it is known as mutual inductance.	When an electric current is induced in a coil by flux change produced by the same coil, self-inductance occurs.
It involves two coils.	Self-inductance involves one coil.
When the primary current of the coil decreases, the induced current of the other coil opposes the decay of current in the coil.	When the coil’s primary current decreases, the secondary current opposes the decay of current in the coil.
When the primary current of the coil increases, the induced current of the other coil opposes the increase of current in the coil.	When the primary current of the coil increases, the secondary current opposes the increase of current in the coil.
The mutual inductance formula is	The formula for self-inductance is L= N∅ /I.

Examples

The main principle that helps function transformers, generators, motors, etc., is mutual inductance.
An electric dryer uses mutual inductance.
All the equipment deals with magnetic fields.

Conclusion

Mutual inductance can be described as the electromotive force induced when one coil’s magnetic field opposes the change of voltage and current in another coil. The coils become magnetically linked due to changes in magnetic flux. Henry is the SI unit of inductance. It is denoted by H. When the primary current of the coil decreases, the induced current of the other coil opposes the decay of current in the coil. When the primary current of the coil increases, the induced current of the other coil opposes the increase of current in the coil. Examples are transformers, electric motors, generators, etc.