What are the Mutual Inductance Implications in Physics, and How Do They Work?

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,  ØB ∝ 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, 

NØB ∝ 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: 

M = (μ0.μr.N1.N2.A)L

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= 4𝜋10-2

μr = 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.

 Working of Mutual Inductance

• 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 S1 and 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. 

Implications of Mutual Inductance

The implications of mutual inductance 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. 
• Mutual inductance is the property of a coil that is responsible for influencing or modifying the current and voltage in the secondary coil. 
• The implication of mutual induction is the main reason for the formation of eddy current and generation in the test material. 

Factors that Affect the Implications of 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.
• The implication of mutual inductance is also affected by the medium of permeability between the two coils.

Characteristics of Mutual Inductance

• 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.
• The main disadvantage of mutual inductance 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 mutual inductance that takes place. 
• The mutual inductance of coils 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

Examples of Mutual Inductance

• 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 of mutual inductance are transformers, electric motors, generators, etc.