$[0/4$ Points$]$

SERPSE$1028\mathrm{.}5.$OP$\mathrm{.}023.$

A certain electric motor consists of a thin rectangular coil of current$-$carrying wire that rotates in the presence of a uniform magnetic field of magnitude $0\mathrm{.}800$ T $.$ The coil has $84$ turns of wire, and is $2\mathrm{.}37$ cm wide by $4\mathrm{.}41$ cm long. When the coil is oriented so that the plane of the rectangle is perpendicular to the magnetic field, it carries a current of $10\mathrm{.}5$ mA $,$ and its magnetic dipole moment points in the opposite direction of the magnetic field. The coil then rotates one half revolution, and the direction of its dipole moment is then flipped so that the process repeats itself. In this way, the coil continues to rotate at an angular speed of $3\mathrm{.}72{10}^{3}re\frac{v}{m}in.$

$($a$)$ What is the maximum torque acting on the coil $($in $N*m)?($Enter the magnitude.$)$

$N*m$

$($b$)$ What is the peak power output of the motor $($in W $)?$

$$

w

$($c$)$ How much work $($in J$)$ is performed by the magnetic field on the rotor in every full revolution?

$$ J

$($d$)$ What is the average power of the motor $($in W$)?$

$$ w