Question

A long, thick cylindrical conductor of radius a-20 mm, charged with a surface charge density ps 0.01 C/m2, is located in free space. Calculate the energy stored per unit length of the conductor within a radius b - 100 m from the conductor. Indicate your answer in J/m

Answer 1

A long thick cylinder conductor radius a = 20 mm = 20 times 10^-3 mm surface change density f_s = 0.01 c/m^2 Energy stored per unit length (W) = ? Now energy W = 1/2 integral E_0 E^2 dA Where E = electric field intensity Note Consider the cylindrical shell and construct a Gaussian cylindrical of length L and surface charge density f_s. Due to symmetry the electric field must of only point in the r^vector direction and is a function of 'v' only for r > a, Gaussian Law implies \r\n that the electric Field is zero For r > Q the charge enclosed is theta = 2 Pi QL soVertical-bar E Vertical-bar 2 Pi rL = theta/60 y E = a 6_s/r epsilon_0 a_n^^ So that E^bar = {f_s a/r epsilon_0 a_n^^: 0 < r < a a < r < b r > b} W_E = epsilon_0/2 integral E^2 dA = epsilon_0 integral^infinity_0 Pi^2 E^2 dr