Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross-sectional area A = 10 cm² and length = 20 cm. If one of the solenoid has 300 turns and the other 400 turns, their mutual inductance is (μ₀ = 4π × 10⁻⁷ T m A⁻¹) (a) 2.4π × 10⁻⁵ H (b) 4.8π × 10⁻⁴ H (c) 4.8π × 10⁻⁵ H (d) 2.4π × 10⁻⁴ H

Answer: (d). For coaxial solenoids on the same pipe: M = (μ₀ N₁ N₂ A)/(l) M = 4π×10⁻⁷× 300 × 400 × 10×10⁻⁴0.20 M = 4π×10⁻⁷× 600 = 2.4π×10⁻⁴ H So the answer is (d).

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Mutual Inductance

Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross-sectional area $A = 10\text{ cm}^2$ and length $= 20\text{ cm}$ . If one of the solenoid has $300$ turns and the other $400$ turns, their mutual inductance is

$\left(\mu_0 = 4\pi \times 10^{-7}\text{ T m A}^{-1}\right)$

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Answer: (d)

For coaxial solenoids on the same pipe: $M = \frac{\mu_0 N_1 N_2 A}{l}$
$M = \frac{4\pi\times10^{-7}\times 300 \times 400 \times 10\times10^{-4}}{0.20}$
$M = 4\pi\times10^{-7}\times 600 = 2.4\pi\times10^{-4}\text{ H}$
So the answer is (d).

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