Consider two coaxial cylinders of same length L, with vacuum inside them. The radii of the inner solenoid and the outer solenoid are r1 and r2 (> r1), respectively. The number of turns per unit length are n1 and n2 for the inner solenoid and the outer solenoid, respectively. The mutual inductance is:

1
π μ0  n1 n2 \(\rm r_2^2\) L
2
π μ0 n1 n2 \(\rm r_1^2\) L
3
4π μ0  n1 n2 \(\rm r_1^2\) L
4
4π μ0  n1 n2 \(\rm r_2^2\) L
5
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