Current:

$\overline{){\mathbf{i}}{\mathbf{=}}\frac{\mathbf{N}\mathbf{\pi}{\mathbf{r}}^{\mathbf{2}}}{\mathbf{R}}{\mathbf{\left(}}\frac{\mathbf{d}\mathbf{B}}{\mathbf{d}\mathbf{t}}{\mathbf{\right)}}}$

N is the number of turns, r is the radius of the coil, R is the resistance, and dB/dt is the derivative of the magnetic field with respect to time.

$\frac{\mathbf{d}\mathbf{B}}{\mathbf{d}\mathbf{t}}\mathbf{=}\frac{\mathbf{d}}{\mathbf{dt}}\mathbf{(}\mathbf{0}\mathbf{.}\mathbf{02}\mathbf{t}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{010}{\mathbf{t}}^{\mathbf{2}}\mathbf{)}$

A 5.0-cm-diameter coil has 20 turns and a resistanceof 0.50 ohms. A magnetic field perpendicular to the coil is B =0.02t + 0.010t^{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.

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