Problem #$2(30$ Points$)$ In the figure below, a metal wire of mass $m=20\mathrm{.}8mg$ can slide with negligible friction on two horizontal parallel rails separated by distance $d=3\mathrm{.}17cm.$ The track lies in a vertical uniform magnetic field of magnitude $49\mathrm{.}1$ mT $.$ At time $I=0s,$ device G is connected to the rails, producing a constant current $i=6\mathrm{.}05mA$ in the wire and rails $($even as the wire moves$).$ At $t=78\mathrm{.}2ms,$ what are the wire's $($a$)$ speed $(25$ points$)$ and $($b$)$ direction of motion $(5$ points$)?$ show work please.