A $5\mathrm{.}0-$cm$-$diameter coil has $20$ turns and a resistance of $0\mathrm{.}500\mathrm{.}50.$ A magnetic field perpendicular to the coil is B$=0\mathrm{.}020$t$+0\mathrm{.}010$t$2$B$=0\mathrm{.}020$t$+0\mathrm{.}010$t$2,$ where BB is in tesla and tt is in seconds. Find an expression for the induced current I$($t$)$I$($t$)$ as a function of time.

Part A

Find an expression for the induced current I$($t$)$I$($t$)$ as a function of time.

Express your answer in terms of the variable tt$.$