A$7.$A semicircle wire of radius $\backslash (\backslash$mathrm$\{$a$\}=4\mathrm{.}00\backslash$mathrm$\{$~cm$\}\backslash )$is rotated at constant angular speed $30\mathrm{.}0$revoultions per minute in a uniform $20\mathrm{.}0$mT magnetic field as shown in Figure A$7.$

Figure A$7$

$($a$)$Determine the frequency of the induced emf in the loop.

$($b$)$Determine the amplitude of the induced emf in the loop