$(20\%)$ An infinitely long solenoid with air core having a radius a and $n$ closely wound turns per unit length, as shown in the figure. The windings are slanted $()$ at an angle $$ and carry a current I.

$($a$)$ Find the $z-$component of the magnetic flux density $(B_z)$ both inside and outside the solenoid. $(10\%)[$Hint: Use Ampere's law.$]$

$($b$)$ Find the $-$component of the magnetic flux density $(B_{})$ both inside and outside the solenoid. $(10\%)[$Hint: Use cylindrical coordinates, $r,,z.]$