A rectangular loop of wire with total resistance $R=800$ is fixed in place near an infinitely long straight current carrying wire as shown in the figure. If the current in the wire is decaying at $I(t)=(500A)e^{-(\frac{t}{5\mathrm{.}0}s)}$

a$.$ Find the flux through the loop as a function of time and its value at $t=10\mathrm{.}0s.$

b$.$ Find the induced current in the loop as a function of time and at $t=10\mathrm{.}0s.$ State whether it is clockwise or counterclockwise.