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Question:

There are two long coaxial solenoids of same length l. The inner and outer coils have radii r1 and r2 and number of turns per unit length n1 and n2 respectively. The ratio of mutual inductance to the self-inductance of the inner coil is:

n2n1.r22r21

n2n1.r1r2

n1n2

n2n1

Solution:

M=μ₀n₁n₂πr₁²L
L₁ = μ₀n₁²πr₁²L
M/L₁ = n₂/n₁