Two concentric circular coils of radii 1 cm and 1000 cm, with 10 and 200 turns respectively, are coaxial with coinciding centres. The mutual inductance is ______ × 10⁻⁸ H. [Take π² = 10]
Physics · Circular Motion
JEE Mains 6 April 2023 Shift 2 Evening Shift

Question

Two concentric circular coils of radii 1 cm and 1000 cm, with 10 and 200 turns respectively, are coaxial with coinciding centres. The mutual inductance is ______ × 10⁻⁸ H. [Take π² = 10]

G1 Physics · Accepted Answer

Because the larger coil radius is much greater than the smaller coil radius, the magnetic field produced by the large coil is nearly uniform over the small coil. Field at the centre of the large coil: B = μ₀N₂I/(2R₂) Flux through one turn of the small coil: Φ = BπR₁² Total flux linkage with the small coil: N₁Φ Therefore mutual inductance: M = N₁Φ/I = μ₀N₁N₂πR₁²/(2R₂) Given: N₁ = 10 N₂ = 200 R₁ = 0.01 m R₂ = 10 m Using μ₀ = 4π×10⁻⁷ and π² = 10: M = 4×10⁻⁸ H Final value: 4