Date of Award
Master of Science
Dr. David J. Jeffrey
This thesis calculates the potential resulting from a sphere placed inside of a cylinder of infinite length with a uniform field imposed at infinity. We start with a general discussion on axial and general multipoles in physics. We discuss how a potential function can be found by solving the Laplace equation in spherical or cylindrical coordinates and how this technique is equivalent to finding the multipoles. We calculate the potential resulting from a sphere placed inside of a cylindrical tube. We do this by transferring multipoles expressed in cylindrical coordinates to spherical coordinates. The strengths of the multipoles are obtained as power series in the ratio of the radii of the sphere and the cylinder. The dipole strength of the sphere gives the increase of the potential drop along the cylinder. The presence of this sphere is electrically equivalent to increasing the length of the cylindrical tube. The new feature of this solution is the possibility of obtaining the analytic form of the singular behaviour of the solution.
Campbell, Steve W., "Multipole Methods in Potential Theory" (2008). Digitized Theses. 4362.