Within the green dashed circle shown in the figure below, the magnetic field changes with time according to the expression $B=5\mathrm{.}00t^3-1\mathrm{.}00t^2+0\mathrm{.}800,$ where $B$ is in teslas, $t$ is in seconds, and $R=2\mathrm{.}45cm.$

$($a$)$ When $t=2\mathrm{.}00s,$ calculate the magnitude of the force exerted on an electron located at point $P_1,$ which is at a distance $r_1=4\mathrm{.}90cm$ from the center of the circular field region.

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$($b$)$ When $t=2\mathrm{.}00s,$ calculate the direction of the force exerted on an electron located at point $P_1,$ which is at a distance $r_1=4\mathrm{.}90cm$ from the center of the circular field region.

tangent to the electric field line passing through point $P_1$ and clockwise

tangent to the electric field line passing through point $P_1$ and counterclockwise

The magnitude is zero.

$($c$)$ At what instant is this force equal to zero? $($Consider the time after $t=0s.)$

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