In a three$-$dimensional space there is a square coil of N$=2$ loops in the xy plane $($that covers the area from x$=0$ to x$=$x$\_$f and y$=0$ to y$=$y$\_$f at z$=0)$ and a magnetic field that depends both on time and position B$=($Ay$($z$^2)($t$^3)$i$-$hat $+$ B$($x$^2)$y$($t$^2)$j$-$hat $+$Cx$($y$^2)$tk$-$hat$)$T$.$

$1.$Draw a figure visualizing this three$-$dimensional space. Include all three axes and the coil's location.

$2.$ Determine the net magnetic flux through the loop.

$3.$ What is the emf magnitude and direction induced in the coil? State which reference frame you are looking from when determining the direction of the current$/$emf$.$

$4.$ The wire that creates the loop has a circular cross sectional area, with radius r$=0\mathrm{.}815$mm$,$ and is made of silver $($ $=1\mathrm{.}59$x$10^-8$ ohms$*$m$).$ What is the power generated by this system?