(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

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a and b 

(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.
Transcribed Image Text:(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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