P$11$: A coil $4\mathrm{.}00$ cm in radius, containing $500$ turns, is placed in a uniform magnetic field that varies with time according to B $=(0\mathrm{.}012$ T$/$s$)$t $+(3$ x $105$ T$/$s$4)$t$4.$ The coil is connected to a $600$ W resistor, and its plane is perpendicular to the magnetic field. The resistance of the coil can be neglected. Please answer each of the following questions. a$)$ Find the magnitude of the induced emf in the coil as a function of time. b$)$ What is the magnitude of the current in the coil at t $=5$ s$.$