A coil $4\mathrm{.}05$ cmcm in radius, containing $470$ turns, is placed in a uniform magnetic field that varies with time according to B$=($B$=(1\mathrm{.}20102$ T$/$sT$/$s $)$t$+()$t$+(3\mathrm{.}25105$ T$/$s$4$T$/$s$4)$t$4.)$t$4.$ The coil is connected to a $680$ 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.

E$=$E$=9\mathrm{.}25103$ VV $+(+(1\mathrm{.}00104$ V$/$s$3$V$/$s$3)$t$3)$t$3$E$=$E$=2\mathrm{.}91102$ VV $+(+(7\mathrm{.}87105$ V$/$s$3$V$/$s$3)$t$3)$t$3$E$=$E$=2\mathrm{.}91102$ VV $+(+(3\mathrm{.}15104$ V$/$s$3$V$/$s$3)$t$3)$t$3$E$=$E$=9\mathrm{.}25103$ VV $+(+(3\mathrm{.}15104$ V$/$s$3$V$/$s$3)$t$3)$t$3$