$9.($A$)$ A loop with area $\backslash (3\mathrm{.}00\backslash$times $10^\{-2\}\backslash$mathrm$\{$~m$\}^\{2\}\backslash )$ is in a region where there exists a uniform magnetic field with magnitude $4\mathrm{.}00$ T $.$ Initially the field makes an angle of $\backslash (30^\{\backslash$circ$\}\backslash )$ with the plane of the loop. The loop is now rotated clockwise, in a time of $0\mathrm{.}08$ seconds, from this position to where the plane of the loop now makes an angle of $\backslash (57^\{\backslash$circ$\}\backslash )$ with the field.

$($i$)$ In the space provided above, draw showing the final orientation of the field and the loop and the direction of the induced current in the loop. On this diagram also indicate the direction of the induced magnetic field.

$($ii$)$ Solve for the average emf induced in the loop during this rotation.