# What is Mutual Inductance and Self Inductance ?

The mutual and self inductance are concepts in electromagnetism that relate to the behaviour of coils or inductors in an electrical circuit. The Self and mutual inductance formula are as follows.

Self inductance : It is a property of an individual coil or inductor that quantifies its ability to
oppose any change in current flowing through it. The self inductance formula is as follows.

L = (Φ/I)

Where,

L = Self inductance in henrys (H)

Φ = Magnetic flux linked with the coil in webers (Wb)

I = Current flowing through the coil in amperes (A)

Mutual inductance : It describes ability of one coil to induce an electromotive force (EMF)
or voltage in another coil when they are placed close to each other and current in one coil
changes. The mutual inductance formula is as follows.

M = Φ_{2}/I_{1}

Where,

M = Mutual inductance in henrys (H)

Φ_{2} = It is the magnetic flux linked with second coil due to current
in the first coil in webers (Wb)

I_{1} = Current flowing through the first coil in amperes (A)

It can also be expressed using magnetic flux linked with the first coil as follows.

M = Φ_{1}/I_{2}

Where,

Φ_{1} = It is the magnetic flux linked with first coil due to current in the
second coil in webers (Wb).

I_{2} = Current flowing through the second coil in amperes (A)

Calculation of mutual inductance between two coils is useful for several reasons in the
field of electronics and electrical engineering as follows.

1. It helps to predict change in current in one coil will induce how much voltage in the other
coil.

2. It is used in transformer design, coupled inductor based filter design and
to minimize crosstalk and interference between components.

3. It is fundamental in wireless charging technologies.

4. It is used in NFC and RFID readers.

5. Accurate knowledge of mutual inductance helps in design of antenna arrays for specific
applications.

## Mutual Inductance calculator

EXAMPLE#1 Mutual Inductance calculator as per formula-1 mentioned below:

INPUTS: self inductance of 1st coil= 75 mH , self inductance of 2nd coil= 50 mH, Coupling factor = 0.75

OUTPUT: Mutual Inductance = 45.92 mH

## Mutual Inductance Formula

The mutual inductance (M) between two coils can also be calculated based on
their self inductances (L1 and L2) and coupling factor (k) between them using
following formula.

M = k * (L1 * L2)^{0.5}

This formula assumes ideal coupling between the coils, where all of the magnetic flux generated by one coil links with the other coil. The coupling factor, k, accounts for the actual level of coupling between the coils, which can be less than ideal due to physical separation, orientation, or other factors. If the coils are perfectly coupled (all the magnetic flux from one links with the other), k would be equal to 1. The another mutual Inductance formula is mentioned below.

**Conclusion** : The mutual inductance formula and its associated calculator allows
engineers to perform quick and accurate calculations, which are essential for designing, optimizing, and troubleshooting
various electrical and electronic systems. It helps them make informed decisions about component placement, impedance matching,
energy transfer efficiency, and interference mitigation, ultimately leading to better-designed
and more reliable products and systems.