Two long, coaxial solenoids are arranged one inside the other as shown in the diagram. The inner solenoid has radius \(R_1\), turn density \(n_1 = 3n_0\), and carries current \(I_0\) counterclockwise as viewed from the right end. The outer solenoid has radius \(R_2 > R_1\), turn density \(n_2 = n_0\), and carries current \(2I_0\) clockwise as viewed from the right end. Let \(B_{\text{I}}\) be the magnitude of the net magnetic field at a radial distance \(r < R_1\), and let \(B_{\text{II}}\) be the magnitude of the net magnetic field at a radial distance \(R_1 < r < R_2\). What is the ratio \(\dfrac{B_{\text{I}}}{B_{\text{II}}}\)?