STANDARD Physics Mutual Inductance MCQ Question
A solenoid of length 30 cm with 10 turns per centimetre and area of cross-section 40 cm² completely surrounds another co-axial solenoid of same length, area of cross-section 20 cm² with 40 turns per centimetre. The mutual inductance of the system is
10 H
8 H
3 mH
30 mH
Correct Answer
Detailed Explanation
Mutual inductance of the system, M = μ₀n₁n₂A₂l, where A₂ is the area of inner solenoid. n₁ = 10 cm⁻¹ = 1000 m⁻¹, n₂ = 40 cm⁻¹ = 4000 m⁻¹, l = 30 cm = 30 × 10⁻² m, A₂ = 20 cm² = 20 × 10⁻⁴ m². M = 4π × 10⁻⁷ × 1000 × 4000 × 20 × 10⁻⁴ × 30 × 10⁻² = 301.44 × 10⁻⁵ H = 3 mH.
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