A parallel plate capacitor contanins a mica sheet (thickness ` 0. 5+xx10^(-3) m`) . And a sheet of fiber (thickness `0. 5 xx 10^(-3) m`) . The dielectric constant of mica is `8` and that of thye fiber is `2.5` Assuming that the fiber breaks down when subjected to an electric field of ` 6.4 xx 10^6 Vm^(-1)`. , find the maximum safe voltage that can be applied to the capacitor.

Explanation

Let `sigma` be the surface charge density of capacitor plates.
for mica `E_(1) = (sigma)/(K_(1) in_(0))`
and for fibre `E_(2) = (sigma)/(K_(2) in_(0)) or (E_(1))/(E_(2)) = (K_(2))/(K_(1))`
As `E_(2) = 6.4xx10^(6) V//m`
`E_(1) = (K_(2))/(K_(1)) xx E_(2) = (2.5)/(8) xx 6.4xx10^(6) = 2xx10^(6) V//m`
Maximum voltage for capacitor
`V = E_(1) d_(1) + E_(2) d_(2) = 2xx10^(3) + 3.2xx10^(3) = 5200V`