Solenoid
Binside-short = ? mo n I [cos(qR) - cos(qL)]
Note that in both cases, we have mo and I in the numerator. But where is the inverse distance? It is inside the n (n = N/L)!
Note that the radius for a long solenoid doesn’t matter. For a short solenoid, the radius and length are both involved in the angles qR and qL.