A single circular loop of wire with radius $2\mathrm{.}40$ cm lies in the xy$-$plane. There is a uniform magnetic field that changes at a steady rate from $0\mathrm{.}140$ T in the $+$z$-$direction at t $=0$ to $0\mathrm{.}110$ T in the $-$z$-$direction at t$=2\mathrm{.}00$s$.$ Take the area vector for the loop to be in the $+$z$-$direction. Find the magnetic flux through the loop at t $=0.$ Find the magnetic flux through the loop at t$=2\mathrm{.}00$s$.$ Find the magnitude of the induced emf in the loop while the field is changing.