A dielectric material with a relative permittivity ${}_r=6$ and dielectric strength of $20M\frac{V}{m}$ is placed in a parallel plate capacitor. The plates are separated by $0\mathrm{.}5$ mm $,$ and plate area is $0\mathrm{.}02m^2.$

$($a$)$ Determine the delectric breablown voltage of the capaciter.

$($b$)$ Calculate the masimum capacitance of the capacitor.