$2.$ A circular plate capacitor, radius $\backslash ($ b $\backslash )$ and inter$-$plate distance $\backslash ($ s $\backslash )(\backslash ($ s $\backslash$ll b $\backslash )$ so we can neglect $\backslash (\backslash$vec$\{$E$\}\backslash )$ field outside$),$ in a closed circuit is connected by two wires to the center of each disks and is charged to initial potential difference of $\backslash ($ V $\backslash ).$ Consider position $\backslash ($ P $\backslash )$ at the center of the gap and distance $\backslash ($ r $\backslash )$ above the axis. Assume the other part of the circuit has an equivalent resistance $\backslash ($ R $\backslash )$ and the capacitor start to discharge at time $\backslash ($ t$=0\backslash ).$

$($a$)$ Find the electric current $\backslash ($ I$($t$)\backslash )$ as a function of time. $(10$ pts$)$

$($b$)$ Find the magnetic field $\backslash (\backslash$overrightarrow$\{\backslash$boldsymbol$\{$B$\}\}($r$,$ t$)\backslash )$ at position $\backslash ($ P $\backslash ).($both $\backslash ($ r