$8.$ Two long parallel current$-$carrying wires $\backslash ($ P $\backslash )$ and $\backslash ($ Q $\backslash )$ are separated by $0\mathrm{.}10$ m $.$ The current in wire $\backslash ($ P $\backslash )$ is $5\mathrm{.}0$ A $.$

The magnetic force on a length of $0\mathrm{.}50$ m of wire P due to the current in wire Q is $\backslash (2\mathrm{.}0\backslash$times $10^\{-5\}\backslash$mathrm$\{$~N$\}\backslash ).$

$($a$)$

State and explain the magnitude of the force on a length of $0\mathrm{.}50$ m of wire Q due to the current in P $.$

$($b$)$

Calculate the current in wire Q$.$

$($c$)$

Another current$-$carrying wire $\backslash ($ R $\backslash )$ is placed parallel to wires $\backslash ($ P $\backslash )$ and $\backslash ($ Q $\backslash )$ and halfway between them as shown.

The net magnetic force on wire Q is now zero.

$($c$.$i$)$

State the direction of the current in R$,$ relative to the current in P $.$