solenoids, A and $B,$ ane wound using equal lengths of the same kind of wire. The length of the axis of each solenoid is large compared with its diameter. The axial length of $A$ is twice as large as that of $B,$ and A has twice as many turns as $B.$ What is the ratio of the inductance of solenoid $A$ to that of solenoid $B?$

$4$

$2$

$\frac{1}{2}$