A parallel plate capacitor has square plates of side length L kept at a separation d. The space between them is filled with a dielectric whose dielectric constant changes as `K = e^(betax)` where `x` is distance measured from the left plate towards the right plate, and b is a positive constant. A poten- tial difference of V volt is applied with left plate positive.
(i) What happens to capacitance of the capacitor if d is increased ? What is the smallest possible capacitance that can be obtained by changing d ?
(ii) Write the expression of electric field between the plates as a function of `x`.

Answer

(i) Capacitance decreases, `C_(min) = in_(0) L^(2) beta`
(iii) `E=(betaVe^(-betax))/(1-e^(=-betad))`