A coil $3\mathrm{.}70$ cm radius, containing $430$ turns, is placed in a uniform magnetic field that varies with time according to B$=(1\mathrm{.}20\backslash$times $10-2($ T$)/($s$))$t$+(3\mathrm{.}40\backslash$times $10-5($ T$)/($s$)4)$t$4.$ The coil is connected to a $540-\backslash$Omega resistor, and its plane is perpendicular to the magnetic field. You can ignore the resistance of the coil.

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

E$=7\mathrm{.}06103$ V $+(8\mathrm{.}01105$ V$/$s$3)$t$3$E$=2\mathrm{.}22102$ V $+(6\mathrm{.}29105$ V$/$s$3)$t$3$E$=2\mathrm{.}22102$ V $+(2\mathrm{.}52104$ V$/$s$3)$t$3$E$=7\mathrm{.}06103$ V $+(2\mathrm{.}52104$ V$/$s$3)$t$3$

What is the current in the resistor at time t$0=4\mathrm{.}65$ s $?$