STANDARD Physics Mutual Inductance MCQ Question
Two conducting circular loops of radii R₁ and R₂ are placed in the same plane with their centres coinciding. If R₁ > R₂, the mutual inductance M between them will be directly proportional to
R₁/R₂
R₂/R₁
R₁²/R₂
R₂²/R₁
Correct Answer
Detailed Explanation
Let a current I₁ flows through the outer circular coil of radius R₁. The magnetic field at the centre of the coil is B₁ = μ₀I₁/2R₁. As the inner coil of radius R₂ placed co-axially has small radius (R₂ < R₁), therefore B₁ may be taken constant over its cross-sectional area. Hence, flux associated with the inner coil is Φ₂ = B₁πR₂² = μ₀I₁πR₂²/2R₁. As M = Φ₂/I₁, M ∝ R₂²/R₁.
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