EXTRA CREDIT: Consider a long straight wire carrying a sinusoidal current $\backslash ($ I$($t$)=$I$\_\{0\}\backslash$sin $(\backslash$omega t$)\backslash ).$ In the plane of the wire is a square loop of edge length $\text{'}$a$\text{'}$ and at distance $\text{'}$d$\text{'}$ from the wire, as shown.

a$.$ Solve for the current in the loop, assuming the wire of the loop has a resistance R$.$

b$.$ When the current I is to the right and increasing, what would the direction of the current induced in a wire loop placed at the position of the square? Explain your reasoning briefly.