There are two long co-axial solenoids of the same length \( l \). The inner and outer coils have radii \( r_1 \) and \( r_2 \) and the number of turns per unit length \( n_1 \) and \( n_2 \), respectively. The ratio of mutual inductance to the self-inductance of the inner coil is:
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The mutual inductance depends on the turns per unit length of both solenoids, while self-inductance depends only on the inner solenoid.