$1.[25$pts$.]$ The capacitor shown in the figure consists of two conducting disks of radius $\backslash ($ R $\backslash ),$ separated by the interval $\backslash ($ d $\backslash ).$ There flows a current $\backslash ($ I$($t$)\backslash )$ along the wire, with the areal charge density $\backslash (\backslash$sigma$($t$)\backslash )$ on the capacitor. Obtain the magnetic field $\backslash ($ B$($t$)\backslash )$ inside the capacitor at the radial position $\backslash (\backslash$frac$\{$R$\}\{2\}\backslash ).($Assume that it is a vacuum with the permeability $\backslash (\backslash$mu$\_\{0\}\backslash )$ inside the capacitor and the interval $\backslash ($ d $\backslash )$ is so small compared to the radial size $\backslash ($ R $\backslash )$ that the electric field is almost uniform inside the capacitor.$)$