s$)$ A conducting wire is formed into a square loop. The internal resistance of the loop is $0\mathrm{.}1.$ The wire loop is placed on the $x-y$ plane in free space with the center of the loop at the origin. The area bounded by the loop is $1m^2,$ and its sides oriented parallel to the $x-$and $y-$axes.

$($a$)$ If the magnetic field intensity in the region is given by

vec$(H)(t)=[\frac{0\mathrm{.}4(hat(x))+0\mathrm{.}6(hat(z))}{{}_0}]cos(2000t)\frac{A}{m},$ where ${}_0=4{10}^{-7}\frac{H}{m}$

Determine the amplitude of the current in the loop. $(20$ points$)$

$($b$)$ If the magnetic flux density in the region is given by vec$(B)=$hat$(z)0\mathrm{.}5cos(60t)T$ and the loop is rotating at $1,800$ revolutions per minute with an axis of rotation along the $x-$axis. Determine the amplitude of the current in the loop. $(30$ points$)$