A $44-$turn rectangular coil with length

$=20\mathrm{.}0$ cm

and width

w $=8\mathrm{.}10$ cm

is in a region with its axis initially aligned to a horizontally directed uniform magnetic field of $730$ mT and set to rotate about a vertical axis with an angular speed of $64\mathrm{.}0$ rad$/$s$.$

$($a$)$ What is the maximum induced emf in the rotating coil?

V

$($b$)$ What is the induced emf in the rotating coil at

t $=1\mathrm{.}00$ s$?$

V

$($c$)$ What is the maximum rate of change of the magnetic flux through the rotating coil?

Wb$/$s