Written Problem $3$ A long cylindrical conducting shell $($inner radius $a=2\mathrm{.}0mm,$ outer radius $b=3\mathrm{.}0mm)$ carries a uniform current, i$.$e$.,$ the current is distributed evenly through the cross section of the shell, of $I_1=1\mathrm{.}0$A that is directed into the page. Another thin long wire, that lies a distance $d=6\mathrm{.}0mm$ to the right of the central axis of the conducting shell, carries some unknown current $I_2$ parallel to the shell that is directed either into or out of the page. $($A cross section of this system is shown in the diagram.$)$

$($a$)$ What must the current $I_2$ be such that the total magnetic field due to the conducting shell and this unknown current is zero at point $P,$ which lies a distance $r=2\mathrm{.}5mm$ to the right of the central axis of the conducting shell?

$($b$)$ What is the direction, into the page or out of the page, of $I_2?$

$($c$)$ For these values of the currents, what is the magnitude and direction of the force per unit length on the wire due to the shell's current?