A parallel plate capacitor has circular plates $12$ cm in radius and the plate separation is $0\mathrm{.}40$ mm$.$ The plate

is connected to a $10$ ohm resistor and is charged with a constant voltage of $12$ V$.$ Based on these values the

voltage as a function of time will be V $($t$)=12$V$(1$ e

$$t$/(1109$

s$)).$

$($a $-2$ points$)$ What is the electric field between the plates after $0\mathrm{.}5$ nanoseconds of charging?

$($b $-4$ points$)$ What is the rate of change of the electric field between the plates $($also at $0\mathrm{.}5$ns$)?$

$($c $-4$ points$)$ What is the magnetic field between the plates $5$ cm from the center $($also at $0\mathrm{.}5$ns$)?$