What Is Mutual Inductance?

The world was first introduced to mutual inductance in 1831 by Sir Henry Joseph. 

Mutual inductance is the measure of induction between two coils. The SI unit for mutual inductance is henry (H), and it is a scalar quantity. A circuit has an inductance of 1 henry when an electric current that changes at the rate of 1 ampere per second passes through a coil and yields 1 volt of electricity in a coil near it. 

Examples of the usage of mutual inductance in our everyday lives include its application in transformers, electric generators, motors, etc.

An Introduction To Mutual Inductance

Mutual inductance takes place when two coils are placed next to each other. Let’s say the two coils are named A and B. Consider a scenario when a current is made to pass through coil A. An electromotive force (EMF) gets induced in the coil kept next to A, i.e. coil B. 

• Coil A, in which the current is produced, is called the primary coil.
• Coil B, in which an EMF gets induced, is called the secondary coil.
• According to the principle of electromagnetic induction, a change in the current produced in the primary coil causes an EMF to be induced in the secondary coil. This is why this phenomenon is known as ‘mutual induction’.
• Mutual inductance is the magnitude of EMF induced between the two coils.

The Constant Of Mutual Inductance

• Let us assume that the current that flows in the primary coil (coil A) is I1 and the magnetic field produced due to the current in the primary coil (coil A) is B1.
  • An increase in the current that flows in coil A (I1 ) will cause an increase in the corresponding magnetic field produced in coil A (B1).

I1 ∝ B1

• Since coil B is kept next to coil A, the magnetic field B1 is going to pass through coil B as well.
• In case the magnetic field B1 is increased, the magnetic flux (ɸ) that passes through coil B will also increase. 

B1 ∝ ɸ

• Hence, we can conclude that:

I1 ∝ B1 ∝ ɸ 

• According to the principle of electromagnetic induction, due to the change in the magnetic flux (ɸ ), the coil B is going to induce an EMF.
• The magnetic flux (ɸ) is thus dependent on the change in the flow of current in the primary coil, and it is directly proportional to I1.

ɸ ∝ I1 

• The constant used to replace the proportionality of these statements in equations is denoted as ‘M’. M represents the mutual inductance of the two coils, A and B. So the equation can now be rewritten as: 

ɸ = M I1.

•  A large value of mutual inductance may or may not be desirable. 
• For example, when using a transformer, it is important that the value of M be large. 
• However, an appliance such as an electric cloth dryer could potentially be harmful if the mutual inductance between its coils is significant, as it could induce a dangerously high-powered EMF on its metal case covering.

The Coefficient Of Mutual Induction

• The SI unit for the coefficient of mutual inductance is henry (H). The mutual inductance coefficient for a given pair of coils equals one henry when:
  • The magnetic flux (ɸ) induced in a coil due to an electric current of one ampere passing through another coil nearby equals one weber.

Or

The magnitude of EMF induced in one of the coils due to a change of current at the rate of one ampere per second in the other coil is one volt.

• The equivalence of one henry can also be represented as

1 H = 1 Wb/A = 1 V/As-1 = 1 Ωs

The Factors Affecting Mutual Inductance

• The number of turns in coils A and B. 

The more the number of turns, the higher the mutual inductance between the two coils.

• The size and shape of both the coils. 

The mutual inductance will differ based on coils of distinct shapes and sizes.

• The distance between the two coils

The mutual inductance will be less if the distance between the two coils is more. If the distance between the two coils is less, the mutual inductance will be more. The magnetic field of the primary coil can meet the magnetic field of the secondary coil when the distance is less, causing more emf to be induced in the secondary coil.

• The medium between the two coils. 

The mutual inductance of the two coils will be least affected if the coils are placed in a medium such as air or vacuum. The medium the coils are placed in affects the mutual inductance of the coils.

The Examples Of Mutual Inductance

The application of the concept of mutual inductance can be found in transformers, electric generators, and motors.

1. Transformers use mutual inductance to induce AC voltage from one coil to another.
2. Mutual inductance also finds its use in pacemakers (used for patients suffering from heart diseases).
3. Digital signal processing is an example of mutual induction where the counter-winding of two coils lowers the mutual inductance between them.
4. A cloth dryer uses coils that are wound in opposite directions. Their combined magnetic fields balance out by cancelling each other, significantly reducing the mutual inductance and drying the clothes effectively.
5. The metal detectors at airports also make use of this concept.

Conclusion

This introduction to mutual inductance gives us an understanding of what it is and how it is used around us. 

Mutual induction is simply the generation of an induced EMF in a coil as a result of current flowing in an adjacent coil. The measure of the EMF induced between these two coils is mutual inductance.

The factors affecting mutual inductance vary with the number of turns in the coils, the size and shape of the coils, and the distance or the medium between the two coils. The examples of mutual inductance are found in many applications in our daily lives, from transformers and electric generators to the metal detectors used in airports.