Choice $2)$ A copper wire carries $2\mathrm{.}25-$A of current in the $+x-$direction $($to the right$)$ as shown in the figure below.

$2$a$)(20$ points$)$ What is the magnitude AND direction of the magnetic field produced by this wire at the position located directly above it labeled $R?$ When reporting the magnetic field direction, be explicit about which right$-$hand rule you applied and how you applied it$.$

$2$b$)(40$ points$)$ Suppose a proton moves parallel to the wire with a constant speed. If this proton were located $64\mathrm{.}1-$cm directly above the wire, how fast AND in which direction would this proton need to be moving in order for its weight to balance the magnetic force acting on it from the wire. For this problem, assume that the acceleration due to gravity on Earth pulls in the $-y-$direction $($down$).$ Again, be EXPLICIT about how you found your velocity direction.

$2$c$)(15$ points$)$ At position $R,$ in which direction$($s$)$ could this proton move so that the wire exerts NO magnetic force on it$?$ Use physics to fully explain your reasoning.

$2$d$)(25$ points$)$ Let's place an insulated rectangular loop $($shown in red$)$ directly on the copper wire; they are arranged so that they lie in the same $x-y$ plane with the copper wire bisecting the rectangular loop as shown in the figure below. Thoroughly explain why the magnetic flux through this loop is $0$ Wb $.$

$25$ A