y axis with a constant angular speed $\backslash$omega $=\backslash$pi ra$($d$)/($s$)$ in a uniform magnetic field B$=2$T

pointing in the positive z direction as shown in the figure. At t$=0$ the loop is in the

xy$-$plane.

$1.$gule $4.1$ ivuicill $1.$

$($a$)$ Write the expression for the magnetic flux through the loop at an instant of time

t$?(4$pt$)$

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

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

$($d$)$ Now the loop is fixed in the xy plane but the magnetic field changes in time as

B$($t$)=$B$\_(0)$e$^(-$at$)$ where B$\_(0)=1$T and a$=2$sec$^(-1).$ What's the magnitude and

direction of the induced emf at t$=1$s $?(8$pt$)$

Bonus: The loop which stays in the xy plane is now crushed to zero area in $\backslash$Delta t$=0\mathrm{.}1$sec in

constant B$=1$T$.$ What's the magnitude of the induced emf in this case? $(3$pt$)$