Question

A straight solenoid has 50 turns per cm in primary and 200 turns per cm in the secondary. The area of cross-section of the solenoid is 4 cm². The mutual inductance is ______.

Options

• 5 × 10^-4 H

• 2 × 10^-4 H

• 3 × 10^-5 H

• 1.5 × 10^-3 H

Answer 1

A straight solenoid has 50 turns per cm in primary and 200 turns per cm in the secondary. The area of cross-section of the solenoid is 4 cm². The mutual inductance is 5 × 10^-4 H.

Explanation:

The relation, gives the magnetic field at any point inside the primary straight solenoid with n₁ turns per unit length carrying a current i₁.

B = μ₀n₁i₁

The magnetic flux through the secondary of N₂ turns each of area S is given as

N₂Φ₂ = N₂(BS) =  μ₀n₁N₂i₁S

∴ m = `("N"_2phi_2)/"i"_1` = μ₀n₁N₂S

Substituting the values,

M = (4π × 10^-7) `(50/10^-2)` (200) (4 × 10^-4)

= 5 × 10^-4 H