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(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 Ep is a constant. Find the value of Eo- (d) Show that the voltage across the capacitor is given by Eo In 1+ Qd and calculate the-capacitance. Find the volume polarization charge density in the dielectrie.

(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 Ep is a constant. Find the value of Eo- (d) Show that the voltage across the capacitor is given by Eo In 1+ Qd and calculate the-capacitance. Find the volume polarization charge density in the dielectrie.

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(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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