The rotating loop in an ac generator is a square $13\mathrm{.}0$ cm on a side. It is rotated at $75\mathrm{.}0$ Hz in a uniform field of $0\mathrm{.}800$ T$.$ Calculate the following quantities as functions of time t$,$ where t is in seconds.

$($a$)$ the flux through the loop

$$B $=$

$$$12\mathrm{.}68$

mT$$m$2$

$($b$)$ the emf induced in the loop

$=$

$6\mathrm{.}358$sin$(471\mathrm{.}2$t$)$

V

$($c$)$ the current induced in the loop for a loop resistance of $2\mathrm{.}00$

I $=$

$3\mathrm{.}179$sin$(471\mathrm{.}2$t$)$

A

$($d$)$ the power delivered to the loop

$=$

$2\mathrm{.}02$sin$2(471\mathrm{.}2$t$)$

W

$($e$)$ the torque that must be exerted to rotate the loop

$=$

mN$$m