A coil $4\mathrm{.}00$cm in radius, containing $500$ turns, is placed in a uniform

magneticfieldthatvarieswithtimeaccordingtoB $=(0\mathrm{.}0120$T $/$s$)$t$+$

$(3\mathrm{.}00105$T $/$s$4)$t$4.$ The coil is connected to a $600$ resistor, and

its plane is perpendicular to the magnetic field. You can ignore the

resistance of the coil. $($a$)$ Find the magnitude of the induced emf

in the coil as a function of time. $($b$)$ What is the current in the

resistor at time t $=5\mathrm{.}00$s$?$

Ans: $0\mathrm{.}0302$V $+(3\mathrm{.}02104$V $/$s$3)$t$3$

$,1\mathrm{.}13104$A