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Question:

A circular coil with a cross-sectional area of 4 cm² has 10 turns. It is placed at the center of a long solenoid that has 15 turns/cm and a cross-sectional area of 10 cm², as shown in the figure. The axis of the coil coincides with the axis of the solenoid. What is their mutual inductance?

9.54µH

7.54µH

8.54µH

10.54µH

Solution:

Given : Number of turns in coil N₂ = 10
Number of turns per unit length in solenoid, n = 15 per cm = 1500 turns per meter
Area of the coil A₂ = 4 cm² = 4 × 10⁻⁴ m²
Mutual inductance M = μ₀nN₂A₂cosθ, where θ is the angle between →B and →A₂
∴M = 4π × 10⁻⁷ × 1500 × 10 × 4 × 10⁻⁴ × 1 (∵ θ = 0°)
⇒M = 7.54 × 10⁻⁶ H = 7.54 µH