A solenoid of length $50 c m$ with $20$ turns per centimeter and area of cross-section $40 c m^{2}$ completely surrounds another coaxial solenoid of the same length, area of cross-section $25 c m^{2}$ with $25$ turns per centimeter. Calculate the mutual inductance of the system.

9.78 m H

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7.85 m H

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8.90 m H

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6.8 m H

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Solution

The correct option is B $7.85 m H$
Let the outer solenoid be $1$ and inverse solenoid be $2$
$\begin{matrix} ∴ l_{1} = 50 c m = 50 \times 10^{- 2} m n_{1} = 2000 t u r n s / m A_{1} = 40 \times 10^{- 4} m^{2} l_{2} = 50 \times 10^{- 2} m n_{2} = 2500 t u r n s / m A_{2} = 2.5 \times 10^{- 4} m^{2} N o w, M_{12} = M_{21} = μ_{0} n_{1} n_{2} A_{2} l = 4 \times 3.14 \times 10^{- 7} \times 2000 \times 2500 \times 50 \times 10^{- 2} \times 25 \times 10^{- 4} = 7.85 \times 10^{- 3} H = 7.85 m H \end{matrix}$
Hence, Option $B$ is correct.

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A solenoid of length 50 cm with 20 turns per centimeter and area of cross-section 40 cm2 completely surrounds another coaxial solenoid of the same length, area of cross-section 25 cm2 with 25 turns per centimeter. Calculate the mutual inductance of the system.

A solenoid of length $50 c m$ with $20$ turns per centimeter and area of cross-section $40 c m^{2}$ completely surrounds another coaxial solenoid of the same length, area of cross-section $25 c m^{2}$ with $25$ turns per centimeter. Calculate the mutual inductance of the system.