(a) Write down the integral and differential forms of Gauss' law in a dielec-tric, defining all quantities used.(b) A parallel plate capacitor is completely filled with a non-conductingdiclectric. Show that the electric displacement, D, is uniform betweenthe plates and calculate its value. (You may assume that the plates eachhave area A and are separated by a small distance d. Each plate carriesa surface charge density a C/m2.)·(c) The diclectric has a non-uniform relative permittivityK(x) = ax + bwhere a andb are constants and x is the perpendicular distance from oneplate. Using Gauss' law, show that the electric field between the platessatisfiesEoE(x) =K(x)-where Eo is a constant. Find the value of Eo-(d) Show that the voltage across the capacitor is given byEoIn 1+QdV =and calculate the-eapacitance.Find the volumme polarization charge density in the dielectric.

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Answered: (a) Write down the integral and…

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(a) Write down the integral and differential forms of Gauss' law in a dielec- tric, defining all quantities used.

College Physics

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ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

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Electric Charges and Fields

One of the fundamental properties is the electromagnetic property. Charge cannot be destroyed by any process and this contributes formally to the law of charge conservation.

Question

(a) Write down the integral and differential forms of Gauss' law in a dielec-
tric, defining all quantities used.
(b) A parallel plate capacitor is completely filled with a non-conducting
diclectric. Show that the electric displacement, D, is uniform between
the plates and calculate its value. (You may assume that the plates each
have area A and are separated by a small distance d. Each plate carries
a surface charge density a C/m2.)·
(c) The diclectric has a non-uniform relative permittivity
K(x) = ax + b
where a andb are constants and x is the perpendicular distance from one
plate. Using Gauss' law, show that the electric field between the plates
satisfies
Eo
E(x) =
K(x)-
where Eo is a constant. Find the value of Eo-
(d) Show that the voltage across the capacitor is given by
Eo
In 1+
Qd
V =
and calculate the-eapacitance.
Find the volumme polarization charge density in the dielectric.

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