In a parallel plate capacitor distance between the plate is 'd'. If dielectric of variable permeability is filled as
`epsilon(x) = epsilon_0 + kx , 0< x le d/2`
`epsilon(x) = epsilon_0 + k(d-x) , d/2 < x le d`
Find capacitance.

Calculate the capacitance of a parallel plate capacitor, with plate area A and distance between the plates d , when filled with a dielectric whose permittivity varies as in(x)=in_(0)+kx(0 lt x lt (d)/(2)), in(x)=in_(0) +k(d-x)((d)/(2) lt x le d) .

The gap between the plates of a parallel-plate capacitor is filled with istropic dielectrc whose permittlvity epsilon varies linearly from espilon_(1) to epsilon_(2) (epsilon_(2) gt epsilon_(1)) in the direction perpendicular to the plates. The area of each plate equals S , the separation between the plates is equal to d . Find : (a) the capacitance of the capacitor, (b) the space density of the bound chagres as a function of a if the charge of the capacitor is q and E in it is directed toward the growing epsilon values.

Calculate the capacitance of a parallel-plate capacitor of area S, separation d and dielectric constant varying linearly from epsilon_(1) " to " epsilon_(2)(epsilon_(2)gtepsilon_(1)) in the direction of the applied field.

For all x epsilon(0,1)

A system of two parallel plates, each of area A, are separated by distance d_(1) and d_(2) . The space between them is filled with dielectrices of permitivities epsilon_(1) and epsilon)_(2) . The permittivity of free space is epsilon_(0) . The equivalent capacitance of the system is

A parallel-plate capacitor has plate area A , the distance between its two plates x and y is d and a dielectric slab of dielectric constant epsilon_(r) is filled between the regions. It is connected to a cell of emf E . If the dielectric slab is removed, then

The separation between the plates of a parallel plate capacitor is d and the area of each plate is A. iff a dielectric slab of thickness x and dielectric constant K is introduced between the plates, then the capacitance will be

Three dielectrics of relative permittivities epsilon_(r_(1))=1,epsilon_(r_(2))=2 , and epsilon_(r_(3))=3 are introduced in a parallel plate capacitor of plate A and B. .

Assertion: The force with which one plate of a parallel plate capacitor is attracted towards the other plate is equal to square of surface density per epsilon per unit area. Reason: The electric field due to one charged plate of the capacitor at the location of the other is equal to surface density per epsilon .