Self and Mutual Inductance Notes & Topics for GATE EE/IES/ISRO/BARC 2019

By BYJU'S Exam Prep

Updated on: September 25th, 2023

In this article, you will find the Study Notes on Self and Mutual Inductance of Simple Configurations which will cover the topic as Introduction, Self-inductance in terms of emf & magnetic flux, Mutual Inductance.

Self Inductance: The property of self-inductance is a particular form of electromagnetic induction.


Self-inductance is defined as the induction of a voltage in a current-carrying wire when the current in the wire itself is changing.


In the case of self-inductance, the magnetic field created by a changing current in the circuit itself induces a voltage in the same circuit. Therefore, the voltage is self-induced.

Self-inductance in terms of emf: A circuit can create changing magnetic flux through itself, which can induce an opposing voltage in itself. The size of that opposing voltage is:

V(opposing) = – L *change in I / change in time

where L is the self-inductance of the circuit, measured in henries.

Self-inductance in terms of Magnetic Flux: A coil carrying current has magnetic flux associated with it. The flux Ф is directly proportional to the current I.

Ф = LI.

Where L is the constant of proportionality, L is called as self Inductance. The ratio of magnetic flux to the current is called as Self Inductance (L).

Mutual Inductance:

  • The changing magnetic field created by one circuit (the primary) can induce a changing voltage and/or current in a second circuit (the secondary).
  • The mutual inductance, M, of two circuits, describes the size of the voltage in the secondary induced by changes in the current of the primary: V(secondary) = – M *change in I (primary) / change in time
  • The units of mutual inductance are Henry, abbreviated “H”.

The magnetic flux through a circuit can be related to the current in that circuit and the currents in other nearby circuits, assuming that there are no nearby permanent magnets.

The magnetic field produced by circuit 1 will intersect the wire in circuit 2 and create current flow.


The induced current flow in circuit 2 will have its own magnetic field which will interact with the magnetic field of circuit 1.

At some point P, the magnetic field consists of a part due to i1 and a part due to i2. These fields are proportional to the currents producing them.

The coils in the circuits are labelled L1 and L2 and this term represents the self-inductance of each of the coils.

The values of L1 and L2 depend on the geometrical arrangement of the circuit (i.e. a number of turns in the coil) and the conductivity of the material. The constant M, called the mutual inductance of the two circuits, is dependent on the geometrical arrangement of both circuits.

In particular, if the circuits are far apart, the magnetic flux through circuit 2 due to the current i1 will be small and the mutual inductance will be small. L2 and M are constants.

We can write the flux, B through circuit 2 as the sum of two parts.

ΦB2 = L2i2 + i1M

An equation similar to the one above can be written for the flux through circuit 1.

ΦB1 = L1i1 + i2M

Though it is certainly not obvious, it can be shown that the mutual inductance is the same for both circuits. Therefore, it can be written as follows:

M1,2 = M2,1

All the Best.

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