A parallel plate capacitor is to be designed which is to be connected across `1kV` potential diffference. The dielectric material which is to be filled between the plates has dielectric constant `K=6pi` and dielectric strength `10^(7) V//m`. For safety the electric field is never to exceed 10% of the dielectric strength . With specifications, if we want to capacitor of capacitance `50pF`, what minimum area (in `mm^(2)`) of plates is required for safe working?
(use `epsilon_(0)=1/(36pi)xx10^(-9)` in S.I. unit)