A parallel plate capacitor is to be designed with a voltage rating 1 kV, using a material of dielectric constant 3 and dielectric strength about `10^(7) Vm^(-1)`. (Dielectric strength is the maximum electric field a material can tolerate without breakdown, i.e., without starting to conduct electricity through partial ionisation.) For safety, we should like the field never to exceed, say 10% of the dielectric strength. What minimum area of the plates is required to have a capacitance of 50 pF?

Explanation

`Elt10^8 rArr 10^3/dlt10^6`
`dgt10^(-3)m rArr C=(kepsilon_0A)/d`
`d=(kepsilon_0A)/Cgt10^(-3)`
`Agt(10^(-3)xxC)/(kepsilon_0)rArr Agt (10^(-3)xx50xx10^(-12))/((6pi)xx1/(36xx10^(-9))=300 mm^2`