Question

the space between the plates of a parallel plate capacitor is fiilled with dielectric constant 11 the electric susceptibility of the medium is​

Answer 1

Capacitance of the vacuum capacitor Co=dAϵo

where A is the area of the plates of capacitor.

Dielectric constant of the medium at a distance xfrom first plate is given by K(x)=Ko+λx

Capacitance of capacitor of thickness dx, dC=dxK(x)Aϵo=dxAϵo(Ko+λx)

Total capacitance C1=∫odAϵo(Ko+λx)dx

Or C1=Aϵo1×λln(Ko+λx)∣∣∣∣∣od

Or C1=Aϵoλ1ln(1+λd/K..