Q.Derive an expression for coefficient of mutual induction of two long coaxial solenoids.

Maximum induced emf = $M\times(di/dt)_{max} = 2\times10^{-2}\times50\pi = \pi$ V.

The emf induced in the secondary coil due to mutual inductance $M$ is

$e = -M\dfrac{di}{dt}$

Given $i = 5\sin(10\pi t)$, so

$\dfrac{di}{dt} = 5\times10\pi\cos(10\pi t) = 50\pi\cos(10\pi t)$

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Mutual inductance M is defined through EMF2 = -M (dI1/dt), and working out the units of this relation gives the henry.

From emf = -M (dI/dt), we get M = emf / (dI/dt), with units volt / (ampere/second) = volt-second/ampere, which is defined as the henry (H).

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Mutual induction — a changing current in one coil inducing an emf in a neighbouring coil — is the working principle behind the transformer and the induction coil.

Mutual induction occurs when a changing current in one coil (primary) sets up a changing magnetic flux that links a nearby second coil (secondary), inducing an emf in it.

Two devices that use this principle:

1. Transformer — used to step up or step down AC voltage, by having primary and secondary windings around a common iron core. …

decreasing (reducing the number of turns per unit length decreases the mutual inductance). …

A transformer transfers electrical energy between two coils purely through the changing magnetic flux linking them — this is mutual induction.

Mutual induction is the phenomenon where a changing current in one coil (primary) induces an emf in a neighbouring coil (secondary) due to the changing magnetic flux linking it, with no direct electrical connection between the coils.

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$1\,\text{H}$: $1\,$A/s rate of current change induces $1\,$V of self-induced EMF.

The self-inductance $L$ of a coil is defined by $\varepsilon = -L\dfrac{dI}{dt}$, relating the self-induced EMF to the rate of change of current through the coil. One henry (1 H) is the self-inductance of a coil in which an EMF of 1 volt is induced when the current through it c …

Mutual inductance is proportional to the product of the number of turns in the two coils.

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This coupling between two coils, where a changing current in one produces an induced emf in the other via the shared changing flux, is called mutual induction.

When the current in one coil (primary) changes, the magnetic flux linked with a nearby second coil (secondary) also changes, inducing an emf in the second coil by Faraday's law — even though there is no direct electrical connection between them. …

True — mutual inductance is measured in henry (H).

Mutual inductance M relates the emf induced in one coil to the rate of change of current in a neighbouring coil: emf = -M (dI/dt). Its SI unit is the henry, where 1 H = 1 volt-second per ampere (1 V s/A). Self-inductance is measured in the same unit. This is …

Mutually induced emf is $\varepsilon = M\,\dfrac{dI}{dt}$; with $M=1\text{ H}$ and the current changing by $1\text{ A}$ in $1\text{ ms}$, $\varepsilon = 1000\text{ V}$.

When the current in one coil changes, it induces an emf in a nearby (mutually coupled) coil, given by

$\varepsilon = M\,\frac{dI}{dt}$

where $M$ is the coefficient of mutual inductance.

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