Sir Henry Joseph gave us the first introduction to self and mutual inductance in 1831. Inductance is one of the most highly regarded concepts in the study of physics. The SI unit for self and mutual inductance is henry (H). One henry is defined as the mutual inductance of a coil for producing an equivalent of one volt when the rate with which the current changes is one ampere per second. The main differences between self and mutual inductance are in the factors affecting inductance, some of which are discussed ahead.

An Introduction to Self-Inductance

It is known that:

• A coil that carries some current is bound to produce a magnetic field
• Whenever the total number of magnetic field lines associated with a coil changes, an electromotive force (EMF) is induced due to electromagnetic induction

Thus, when the current flowing through a coil or circuit changes, a self-induced EMF is created in it. As per a law given by the famous physicist Lenz, self-induced EMF tries to oppose its cause of creation.

This phenomenon of producing a self-induced EMF, which later opposes any change in a coil or a circuit’s electrical state, is known as self-inductance.

An Introduction to Mutual Inductance

Mutual inductance, a fundamental property in the study of physics, talks about two coils 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 EMF is 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 is induced, is called the secondary coil
• A change in the current produced in the primary coil causes an EMF to be induced in the secondary coil, as per the principle of electromagnetic induction
• This is the reason that this phenomenon is known as mutual inductance

Coefficients of Self and Mutual Inductance

1. Self-Inductance

The magnetic flux (ɸ) linked with a coil is directly proportional to the current (I) that flows through it at any particular instance.

ɸ∝ I

To remove the proportionality sign, we can write the equation as:

ɸ = L I

Where L is the constant, also known as the coefficient of self-inductance.

Thus, the coefficient of self-inductance of any coil or circuit may be defined as the magnetic flux associated with it due to a one-ampere current flowing through it.

• The SI unit of L is defined as Volt/(Ampere/sec) = sec – volt/ampere = Ω-sec

2. Mutual Inductance

Due to the change in the magnetic flux of (ɸ2), the secondary coil will induce an EMF. 

Thus, the magnetic flux (ɸ2) is dependent on the change in the flow of current in the primary coil. It is directly proportional to the current (I1).      

ɸ2 ∝ I1 

The proportionality symbol ‘∝’ is replaced by a constant, denoted as ‘M’. This is the mutual inductance of the two coils, A and B.

ɸ2 = M I1 

Hence, the mutual inductance coefficient for a given pair of coils is defined as follows:

• The magnetic flux (ɸ) linked with one of the coils due to a current of one ampere in the other coil 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 Factors Affecting Self and Mutual Inductance

Below are the factors that affect the self-inductance constant ‘L’:

• The geometry of the coils: A coiled arrangement is more likely to trap a larger number of magnetic field lines than a straight wire arrangement
• The nature of the medium between the two coils: If an insulated ferromagnetic material is used as the core of a coil, it is likely to result in more magnetic field lines becoming linked and this, in turn, would raise the value of the coefficient of self-inductance
• The length of the coils: The magnetic flux (ɸ) induced in a longer coil is always less than the flux induced within a shorter coil

Below are the factors affecting the mutual inductance constant ‘M’:

• 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 be different for 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 greater
• 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: In case the coils are kept in a medium, such as air or vacuum, the mutual inductance of the two coils will be less

Examples of Self and Mutual Inductance

Self-inductance finds its applications in the following examples:

• Tuning circuits
• Inductors that are used as relays
• Various sensors
• Induct the ion motors and transformers

Mutual inductance finds its applications in the following examples:

• Transformers use the concept to alter one AC voltage to another
• Mutual inductance finds its use in pacemakers (used for heart patients)
• Digital signal processing is an example wherein mutual inductance is lowered by the counter-winding of coils
• An electric cloth dryer uses coils for heating
• The coils can be wound in a counter manner such that their combined magnetic fields balance out by cancelling each other, significantly reducing the mutual inductance
• Metal detectors at airports also make use of this concept

Differences Between Self and Mutual Inductance