# Cylindrical Capacitor: Gauss Law

Not what you're looking for?

A capacitor consists of two concentric long cylindrical conductors of radii a and c, where c > a, and each is of negligible thickness. The space between the conductors is filled with two layers of dielectric materials. Using cylindrical co-ordinates with z-axis along the axis of the cylindrical conductors, the space a<r<b is filled with an LIH (linear, isotropic and homogeneous) dielectric of relative permittivity e1 and the space b<r<c with a second LIH dielectric of relative permittivity e2 . The cylinders are sufficiently long that end effects can be neglected. The charge per unit length of the inner conducting cylinder (r=a) is lembda, and that on the outer conducting cylinder (r=c) is -lembda.

a) Use the integral version of Gauss's law to find the electric field E and the electric displacement D in the region a < r < c. Hence calculate the electrostatic field energy stored in a length l of the capacitor.

b) Hence find the capacitance of a length l of the capacitor.

(Please see the attachment also)

##### Purchase this Solution

##### Solution Summary

The expert examines cylindrical capacitors for Gauss Laws.

##### Solution Preview

Please refer to the attachment.

a) For the region a < r < b (region 1) : Let us consider a cylindrical Gaussian surface of length L shown in dotted red in the fig. and apply Gauss theorem : ∫E.ds = Q/ε where Q is the total charge enclosed by the Gaussian surface. Here, Q = charge on length L of the inner cylindrical plate = λL

Let E1 be the radially outwards electric field on the curved face of the ...

##### Purchase this Solution

##### Free BrainMass Quizzes

##### The Moon

Test your knowledge of moon phases and movement.

##### Classical Mechanics

This quiz is designed to test and improve your knowledge on Classical Mechanics.

##### Introduction to Nanotechnology/Nanomaterials

This quiz is for any area of science. Test yourself to see what knowledge of nanotechnology you have. This content will also make you familiar with basic concepts of nanotechnology.

##### Basic Physics

This quiz will test your knowledge about basic Physics.

##### Variables in Science Experiments

How well do you understand variables? Test your knowledge of independent (manipulated), dependent (responding), and controlled variables with this 10 question quiz.