In the figure below, a long circular pipe with outside radius $\backslash ($ R$=2\mathrm{.}63\backslash$mathrm$\{$~cm$\}\backslash )$ carries a $($uniformly distributed$)$ current $\backslash ($ i$=9\mathrm{.}33\backslash$mathrm$\{$~mA$\}\backslash )$ into the page. A wire runs parallel to the pipe at a distance of $\backslash (3\mathrm{.}00$ R $\backslash )$ from center to center. Find the $($a$)$ magnitude and $($b$)$ direction $($into or out of the page$)$ of the current in the wire such that the ratio of the magnitude of the net magnetic field at point $\backslash ($ P $\backslash )$ to the magnitude of the net magnetic field at the center of the pipe is $3\mathrm{.}67,$ but it has the opposite direction.

$($a$)$ Number

Units

$($b$)$