Q.The device is based on the principle of mutual induction is -

Mutual Inductance: From Intuition to Definition

Imagine you have two separate coils of wire placed close to each other, but not electrically connected. You connect the first coil to a battery through a switch. The moment you close the switch, current begins to flow in coil 1. That current doesn't just stay in coil 1 — it creates a magnetic field around it. Some of that magnetic field spreads out and passes through the loops of coil 2.

Now, here is the key physical fact: a changing magnetic field through a coil induces an emf (electromotive force) in that coil. So when you close the switch, the current in coil 1 rises from zero to some steady value. During that brief rise, the magnetic field through coil 2 is also changing — from zero to some steady value. That changing field induces a temporary emf in coil 2. If coil 2 is part of a closed circuit, that induced emf will drive a current for as long as the field is changing.

The same thing happens in reverse: if you change the current in coil 2, it induces an emf in coil 1. This mutual influence — the ability of a changing current in one circuit to induce an emf in a nearby circuit — is called mutual inductance.

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The Precise Definition

Let coil 1 carry a current $I_1$. This current produces a magnetic flux $\Phi_{21}$ through each turn of coil 2. The total flux linkage through coil 2 is $N_2 \Phi_{21}$, where $N_2$ is the number of turns in coil 2.

For a given geometry, the flux through coil 2 is directly proportional to the current in coil 1:

The constant of proportionality $M_{21}$ is called the mutual inductance of the pair of coils. The subscript $21$ means "flux in coil 2 due to current in coil 1."

By Faraday's law, the induced emf in coil 2 is the negative rate of change of flux linkage:

The negative sign indicates Lenz's law — the induced emf opposes the change that produces it.

If you reverse the roles — change current in coil 2 and measure the induced emf in coil 1 — you get:

A remarkable fact (which follows from energy conservation) is that the two mutual inductances are equal:

So we simply call it $M$, the mutual inductance of the pair.

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Units and Typical Values

The SI unit of mutual inductance is the henry (H). From the defining equation:

One henry means that a current changing at the rate of 1 ampere per second induces an emf of 1 volt in the other coil. In practice, typical values are much smaller — millihenries (mH) for transformers and microhenries ($\mu$H) for circuits on a circuit board.

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A Simple Example: Two Coaxial Solenoids …