Problem $1$

Metal wire is bent into a circular loop of radius $r=0\mathrm{.}3m.$ The loop is rotating about the $y$ axis with a constant angular speed $=ra\frac{d}{s}$ in a uniform magnetic field $B=2T$ pointing in the positive $z$ direction as shown in the figure. At $t=0$ the loop is in the $xy-$plane.

Figure $4$: Problem $1.$

$($a$)$ Write the expression for the magnetic flux through the loop at an instant of time $t?(4pt).$

$($b$)$ What's the magnitude of the induced emf at $t=0\mathrm{.}5sec?(4$pt$)$

$($c$)$ What's the direction of the induced current in the loop at $t=0\mathrm{.}1sec?(4$ pt $)$

$($d$)$ Now the loop is fixed in the $xy$ plane but the magnetic field changes in time $B(t)=B_0{e}^{-at}$ where $B_0=1T$ and $a=2se{c}^{-1}.$ What's the magnitude ar direction of the induced emf at $t=1s?(8$pt$)$