A coil $4\mathrm{.}40$ cm in radius, containing $560$ turns, is placed in a uniform magnetic field that varies with time according to B$=(1\mathrm{.}20102$ T$/$s $)$t$+(3\mathrm{.}15105$ T$/$s$4)$t$4.$ The coil is connected to a $570$ resistor, and its plane is perpendicular to the magnetic field. You can ignore the resistance of the coil.

Part A

Find the magnitude of the induced emf in the coil as a function of time.

Part B

What is the current in the resistor at time t$0=5\mathrm{.}20$ s $?$ Express your answer with the appropriate units.