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Grade 12th passGeneral Physics

A parralek plate capacitor of area A separated by a distance d between them. It is for with a dielectric which has a dielectric constant that varies by as k(x)=k(1+alpha x). Where x is the distance measured from one of the plate. The total capacitance off the system is given by

Question image for A parralek plate capacitor of area A separated by

swati mohanty

6 Years agoGrade 12th pass

1 Answer

waqar malik

6 Years ago

let ‘d ‘ be the distance between the plates .

at distance x from one plate, E(x)=E(electric field when there is no dielectric)/k(x)

E(x)=E/k(1+alpha x)

Now, p.d. between the plates V=∫E(x).dx

integrating it carefully within the limit of x from ‘0’ to ‘d’ you will get ,

V=E.log(1+alpha.d)/k.alpha...........................1

let C1 be the capacitance without any dielectric,

then, initial capacitance b/w the plates , C1=Q/E.d...................2

now, final capacitance , C=Q/V=Q.k.alpha/E.log(1+alpha.d)

Hence ,from eqn 1 and 2 it is cleared that

C=C1.d.k.alpha/log(1+alpha.d)

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