Q$2.(20$ marks$)$

Shown in Fig. Q$2,$ a metal bar is placed on two parallel conducting rails which are in a distance $\backslash ($ l $\backslash )$ apart. A resistor $\backslash ($ R $\backslash )$ is connected across the rails, and a uniform magnetic field $\backslash (\backslash$vec$\{$B$\}\backslash ),$ pointing into the page, fills the entire region. If the bar moves to the right at speed $\backslash ($ v $\backslash ),$

$($a$)$ Find the current flowing through the resistor and its direction.

$($b$)$ Find the magnetic force imposed on the bar.