A $5\mathrm{.}0-$cm$-$diameter coil has $20$ turns and a resistance of $0\mathrm{.}50.$ A magnetic field perpendicular to the coil is B$=0\mathrm{.}020$t$+0\mathrm{.}010$t$2,$ where B is in tesla and t is in seconds. Find an expression for the induced current I$($t$)$ as a function of time. Evaluate I at t$=5$s$.$ Evaluate I at t$=10$s$.$