Question $3.$ As seen in Figure $3($a$),$ there is a coaxial cable consisting of two sufficiently long coaxial cylinder. The electric current $\backslash ($ I $\backslash )$ flows uniformly in opposite direction to each other on the inner cylinder face and the outer face.

$1)$ Find the self$-$inductance $\backslash ($ L $\backslash ).$ Hint: first find the magnetic flux through the light blue surface.

$2)$ Show that the magnetic energy between two cylinders is equal to $\backslash (\backslash$frac$\{$L I$^\{2\}\}\{2\}\backslash )$ per unit length in the axial direction.