Question

two plane coils having no. of turns 1000 and 2000 and radii 5cm and 10cm respectively are placed coaxially in the same plane. Calculate their mutual inductance.

Answer 1

Explanation:

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Answer 2

Concept Introduction:-

It could take the shape of a word or a numerical representation of a quantity's arithmetic value.

Given Information:-

We have been given that two plane coils having no. of turns $1000$ and $2000$ and radii $5$ cm and $10$cm respectively are placed coaxially in the same plane.

To Find:-

We have to find that their mutual inductance.

Solution:-

According to the problem

number of turns in first coil, $N_{1}=1000$

number of turns in second coil, $N_{2}=2000$

radius of first coil, $r_{\uparrow}=5 \mathrm{~cm}=0.05 \mathrm{~m}$

radius of second coil, $r_{2}=10 \mathrm{~cm}=0.10 \mathrm{~m}$

mutual inductance, $M=?$

Let the current / is passed through the inner coil. A magnetic field $B_{1}=\frac{\mu_{0} N_{1} I}{2 r_{1}}$ is produced inside the inner coil whereas the field outside it is zero. The flux through each turn of inner coil is,

$\begin{aligned}\phi &=B_{1} A_{2} \\&=\frac{\mu_{0} N_{1} I}{2 r_{1}} \times \pi r_{2}^{2}\end{aligned}$

The flux through all turns of inner coil is,

$\begin{aligned}\phi &=N_{2} B_{1} A_{2} \\&=N_{2} \times \frac{\mu_{0} N_{1} I}{2 r_{1}} \times \pi r_{2}^{2} \\&=\frac{\mu_{0} N_{1} N_{2} \pi r_{2}^{2}}{2 r_{1}} \times I\end{aligned}$

So, the mutual inductance is,

$M=\frac{\phi}{I}\\&=\frac{\mu_{0} N_{1} N_{2} \pi r_{2}^{2}}{2 r_{1}} \\&=\frac{4 \pi \times 10^{-7} \times 1000 \times 2000 \times \pi \times(0.10)^{2}}{2 \times(0.05)} \\\therefore L &=0.79 \mathrm{H}$

Final Answer:-

The correct answer is the mutual inductance is $\mathbf{0 . 7 9 ~ H}$.

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