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A solenoid with N1 = 1000 turns, inner radius r1 = 1.0 cm, and length l1 = 50 cm is placed concentrically inside a second coil with N2 = 2000 turns, outer radius r2 = 2.0 cm, and length l2 = 50 cm. Assuming free-space conditions, find the mutual inductance of the arrangement.

1. 1.58 mH
2. 2.53 mH
3. 3.20 mH
4. 4.65 mH

Correct answer: 1.58 mH

Solution

M = mu0 * N1 * N2 * pi * r1² / l = (4*pi*10⁻⁷ * 1000 * 2000 * pi * 10⁻⁴) / 0.5 = 16*pi²*10⁻⁴ / 10 =... evaluates to approximately 1.58 mH.

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