A wire loop consists of a semi$-$circle connected by a straight segement. The radius of the semicircle is $\backslash (\backslash$mathrm$\{$R$\}=0\mathrm{.}4\backslash$mathrm$\{$~m$\}\backslash ).$ A current I of $2$ A flows in this loop as shown.

a$)$ What is the area vector $\backslash (\backslash$vec$\{$A$\}=$A $\backslash$hat$\{$n$\}\backslash )$ of the current loop? $($hint: For the direction, you want to apply the right hand rule: if it helps, stretch the loop to a full circular shape.

b$)$ Assuming a magnetic field, magnitude $\backslash ($ B$=5$ T $\backslash )$ is applied in the $\backslash ($ x $\backslash )-$direction. Calculate the torque on the loop

c$)$ Repeat part b$)$ for a magnetic field $\backslash (\backslash$mathrm$\{$B$\}=5\backslash$mathrm$\{$~T$\}\backslash )$ in the $-$y direction. Does the loop rotate clock$-$wise or counter clock$-$wise when looking at it from the $+$x $($right side of the page$)$ direction? $($Hint remember the torque is a vector in the direction of your thumb, and the curl of your hand is the direction of rotation$).$

d$)$ Repeat part b$)$ for a magnetic field in the $+2$ direction.