# What is the principle of mutual induction

## Mutual induction and mutual inductance with point convention

### Definition of mutual induction

Mutual induction is a phenomenon when a coil in EMF is induced due to changing current in the neighboring coil in such a way that the flow of one coil current maintains the connection of another coil.

### Definition of mutual inductance

**Mutual inductance** is the ratio between induced emf across one coil and the rate of change of current in another adjacent coil, such that two coils have the possibility of flux connection.

### Mutual induction

Whenever there is time varying current in a coil, the time varying flux connects to the coil itself and causes a self induced emf across the coil. This emf is viewed as a voltage drop across the coil or inductance. However, it is not practical for a coil to be tied to only its own changing flux. If a time-varying current flows in another coil that is close to the first, the flux generated by the second coil can also connect the first. This varying flux connection from the second coil will also induce an EMF across the first coil. This phenomenon is called **mutual induction** and the EMF induced in one coil due to the time-varying current flowing in another coil is called **mutually induced EMF**. If the first coil is also connected to the time-varying source, the net emf of the first coil results from the self-induced and mutually induced emf.

### Coefficient of mutual induction or mutual inductance

Let us consider a coil of self-inductance L._{1} and another coil of self-inductance L._{2}. Now we will also take into account that there is a deep magnetic core that couples these two coils so that all of the flux generated by one coil connects the other coil. This means that no flow is leaking in the system.

Now we apply a time-varying current to coil 1, which keeps coil 2 in open circuit. The voltage induced across coil 1 will be

Now we are going to keep the first coil open and apply temporally varying current in coil 2. Now the flux generated by coil 2 will connect coil 1 through the magnetic core and as a result the EMF induced in coil 1 will be

Here M is the coefficient of mutual induction, or in short mutual inductance. Without disturbing the source on coil 2, we now connect a time-varying current source across coil 1. In this situation there is a self-induced EMF on coil 1 due to its own current and also mutually induced EMF on coil 1 for the current in of coil 2. Thus, the resulting emf is induced in coil 1

Mutually induced emf can be either additive or subtractive depending on the polarity of the coil. The expression of M is

This term is only justified on the whole, flux generated by one coil will connect another coil, but in practice it is not always possible to connect all of the flux from one coil to another. The value of the actual mutual inductance depends on the actual amount of flux of a coil connection. Here k is a coefficient that needs to be multiplied by M to derive the actual value of the mutual inductance.

### Point Agreement

Since we have already said that, whether the mutually induced EMF would be additive or subtractive and depends on the relative polarity of the coils coupled together. The relative polarity of two or more coils coupled together is denoted by point correspondence. It is shown with a dot mark on both ends of a coil. If at any one time current is entering one coil through a punctured end, then the mutually induced emf on the other coil will have the positive polarity at the punctured end of the latter. In another way it can be said that when the current leaves one coil through the dotted end, the mutually induced emf on the other coil will have the negative polarity at the dotted end of the latter.

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