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)
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 between coils

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 = Φ2/I1
M = Mutual inductance in henrys (H)
Φ2 = It is the magnetic flux linked with second coil due to current in the first coil in webers (Wb)
I1 = 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 = Φ1/I2
Φ1 = It is the magnetic flux linked with first coil due to current in the second coil in webers (Wb).
I2 = 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

Self Inductance of 1st coil in milli Henrys (input1) :

Self Inductance of 2nd coil in milli Henrys (input2) :

Coupling Factor between coils (input3) :

Mutual Inductance in milli-Henrys (output) :

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

Mutual Inductance Formula-1

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.

Mutual Inductance Formula-2

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.

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