Question $2.$ As shown in Figure $4,$ two sufficiently long cylindrical conductors A and B of radii $\backslash ($ R $\backslash )$ are placed distance $\backslash ($ a $\backslash )$ apart.

$1)$ Currents $($ the strength $\backslash ($ I $\backslash ))$ are flowing in conductors A and B in opposite directions to each other. Find the magnetic flux density $\backslash ($ B $\backslash )$ at P on the plane containing the central axis of A and B simultaneously. Note that we suppose $\backslash ($ a $\backslash$gg$>$R $\backslash )$ and the P locates between A and B $.$

$2)$ Assuming that a closed circuit is created by $\backslash ($ A $\backslash )$ and $\backslash ($ B $\backslash ),$ then find the self$-$inductance per unit length.