Question

. Two coils of turns N1 and N2 having current I1 and I2 of length L are coupled on same core having radius r1 and r2 find

the expression for mutual inductance between the coils?

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Answer 1

Given:

Two coils of turns N1 and N2 having current I1 and I2 of length L are coupled on same core having radius r1 and r2.

To Find:

The expression for mutual inductance between the coils?

Solution:

here, it is given that -

Two coils of turns N1 and N2 having current I1 and I2 of length L are coupled on same core having radius r1 and r2.

therefore, let coil be 1 and 2.

then, according to question; mutual inductance between the coils is-

The ratio of magnetic flux through the coil 2 to the current in the coil 1 is called as mutual inductance of coil 1 and coil 2.

$\[{M_{12}} = \dfrac{{{\phi _2}}}{{{I_1}}}\]$

given - coil 1 having turns $N_{1}$ has current $I_{1}$.

Magnetic field inside 1 will be-

$\[\;B = \dfrac{{{\mu _0}{N_1}{I_1}}}{L}\]$

Flux through each turn of coil 2 is-

$\[\begin{gathered} \phi = B \times \pi {r_2}^2 \hfill \\\\ \phi = \frac{{{\mu _0}{N_1}{I_1}\pi {r_2}^2}}{L} \hfill \\ \end{gathered} \]$

Flux through all turns of coil 2 is-

$\[{\phi _2} = \dfrac{{{N_2}({\mu _0}{N_1}{I_1}\pi {r_2}^2)}}{L}\]$

therefore, mutual inductance between the coils is-

$\[M = \dfrac{{\dfrac{{{N_2}({\mu _0}{N_1}{I_1}\pi {r_2}^2)}}{L}}}{{{I_1}}} = \dfrac{{{\mu _0}{N_1}{N_2}\pi {r_2}^2}}{L}\]$     .

Answer 2

Answer:

Hope it help you

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