Boundary-Value Problems in Electrostatics: II — John David Jackson
Physics — E&M · line-charge-conducting-cylinder
Problem
A line charge with linear charge density τ is placed parallel to, and a distance R away from, the axis of a conducting cylinder of radius b held at fixed voltage such that the potential vanishes at infinity. Find
(a) the magnitude and position of the image charge(s);
(b) the potential at any point (expressed in polar coordinates with the origin at the axis of the cylinder and the direction from the origin to the line charge as the x axis), including the asymptotic form far from the cylinder;
(c) the induced surface-charge density, and plot it as a function of angle for R/b=2,4 in units of τ/2πb;
(d) the force per unit length on the line charge.