Question

Two infinitely long conducting hollow cylinders of radius a and b (a < b) are oriented along the z-axis. 1. Compute their capacitance per unit length. 2. Consider the condition (b - a)/a << 1 and compare the capacitance per unit length with that of two infinite conducting plates. 3. Compute the self-capacitance of a conducting cylinder of radius a. The self-capacitance of an object is the capacitance when one of the surfaces is very far away from the other

Answer 1

Given that Two infinitely long conducting hollow cylinder of radius a and b (a < b) are oriented along z-axis (1) V_a = Q/u pi epsilon_0 a V_b = Q/u pi epsilon_0 b potential difference between two conductors Delta = Q/u pi epsilon_0 (1/a - 1/b) = Q/u pi epsilon_0 (b - a)/ab Capacitance = Q/Delta v = u pi epsilon_0 ab/b - a (2) b - a/a lessthanorequalto 1 The u pi ab almostequalto u pi R^2 = A () b + a = d \r\n For two infinite conducting plats c = epsilon_0 A/d so, capacitance is same as Cox admin (3) For a conducting of radius 'a' u = Q/u pi epsilon_0 a C = Q/V = u pi epsilon_0 a C = u pi epsilon_0 a