Problem $4.(10$ pts each, $20$ pts in total$)$ Consider the circuit shown in the figure. A straight wire is placed along the z axis, and carries current $i(t)=10cos200tA.$ A rectangular wire loop is placed parallel to the straight wire, in the yz plane. As shown in the figure, the distance between the loop and the straight wire is d $.$ The width and the length of the rectangular loop is W and L $,$ respectively. The wire loop contains a single resistor R$.$ According to Faraday's Law, the timevarying current $i(t)$ should induce current $i_R(t)$ within the rectangular loop. The parameters are as follows: $d=5mm,W=1cm,L=10cm,R=0\mathrm{.}5.$ All structures are in free space. Calculate:

$($a$)$ At time $t=0s,$ the absolute value and the sign of the current $i_R(t).$

$($b$)$ At time $t=0\mathrm{.}01s,$ the absolute value and the sign of the current of $i_R(t).$