Two coplanar concentric circular loops have radii R₁ and R₂, with R₁ ≫ R₂. Determine the dependence of their mutual inductance M on R₁ and R₂.
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Two coplanar concentric circular loops have radii R₁ and R₂, with R₁ ≫ R₂. Determine the dependence of their mutual inductance M on R₁ and R₂.

G1 Physics · Accepted Answer

Step 1: Mutual inductance is magnetic flux linked to one coil divided by current in the other. Step 2: For two concentric coplanar circular loops with R₁ ≫ R₂, field from larger loop near center is B ≈ μ₀I/(2R₁). Step 3: Flux through smaller loop Φ ≈ BπR₂²; M = Φ/I ≈ μ₀πR₂²/(2R₁) ∝ R₂²/R₁. Answer D, correcting the previous letter C. Final answer: (D) R₂²/R₁.