Solenoid $S_1$ has $N$ turns, radius $R_1$, and length $l$. It is so long that its magnetic field is uniform nearly everywhere inside it and is nearly zero outside. Solenoid $S_2$ has $N_2$ turns, radius $R_2<R_1$ and is of the same length as $S_1$. It lies inside $S_1$ with their axes parallel. Assume $S_2$ carries current $i$. Compute the mutual inductance to which the emf in $S_1$ is proportional.