Magnetic field between two concentric inductors

Question

Suppose we have two inductors with $n_1$ and $n_2$ turns, of radii $R_1$ and $R_2$ $(R_1 > R_2)$ respectively and length $l$. They are aligned concentrically and the smaller inductor is wholly inside the bigger one (i.e. the smaller one doesn't stick out). The currents flowing are $I_1, I_2$ respectively (they might be of different signs to indicate different direction of the current).

The magnetic field inside both indutors (inside the smaller one) is of course homogeneous and equals $B = B_{1_{in}} + B_{2_{in}} = \frac{\mu\mu_0}l(I_1n_1 + I_2n_2)$. But why is the field between these inductors $(r \in (R_2, R_1))$ homogeneous as well and what's its induction value equal?

Answer 1

A Note About A Certain Simplifiation

When we say that the field between these inductors is homogeneous, it's actually a simplification. These inductors have an effectively zero magnetic field outside of them because the field produced from one segment of wire effectively cancels out the field produced from a segment on the other side. This simplification lets us say: outside of an inductor, there is no magnetic field from that inductor.

This simplification breaks down as you get close to the solenoid/inductor. To be more specific, when the distance from one side of the inductor to the other diverges from zero, this simplification no longer holds. In practice, you rarely do anything where this simplification doesn't apply.

The Answer

Given the simplification that the magnetic field produced from a solenoid is zero when outside the coils of that solenoid, you can say that there is no magnetic field from the interior inductor in that space. Therefore it is as if that interior solenoid is not there. Assigning the variables to the larger, exterior solenoid with a subscript 1, you get $B = B_{1_{in}} = \frac{\mu\mu_0}l{I_1n_1}$ when $R_2<r<R_1$.