Solenoid 1 has length \(L_1\), radius \(R_1\), and \(N_1\) turns, and carries a current \(I_1\), producing a magnetic field of magnitude \(B_1\) near its center. Solenoid 2 has length \(L_2 = 2L_1\), radius \(R_2 = 3R_1\), and \(N_2 = 8N_1\) turns, and carries a current \(I_2 = \dfrac{1}{2}I_1\). Both solenoids are sufficiently long relative to their radii to be treated as ideal solenoids. What is the ratio \(\dfrac{B_2}{B_1}\) of the magnetic field magnitude at the center of Solenoid 2 to that at the center of Solenoid 1?