A square loop of side length a$=4\mathrm{.}62$cm is placed a distance b$=1\mathrm{.}01$cm from a long wire carrying a current that varies with time at a constant rate as$,$ I$($t$)=$Qtm where Q$=6\mathrm{.}88$A$/$s is a constant. Part $($a$)$ Find an expression for the magnetic field due to the wire as a function of time at a distance r from the wire in terms of a$,$ b$,$ Q$,$ t$,$ r$,$ and fundamental constants. Part $($b$)$ What is the magnitude of the flux through the loop? Select the correct expression. Part $($c$)$ If the loop has a resistance of $7\mathrm{.}047\mathrm{.}04,$ then what is the induced current, in amperes, that flows in the loop? Part $($d$)$ In what direction does this current flow?