Year: 1991
Type: article
Abstract: Some special cases of the potential for a homogeneous cylinder in a cylindrical coordinate system may be treated by virtue of simple integrals, for example, the potential for a straight rod or wire segment and that for a homogeneous cylinder at the point on its axis. However, because of the involved mathematical operations, the analytical formula of the potential for a homogeneous cylinder at an arbitrary point has not been seen from others. In order to solve the problem, the author has taken the following steps: (1) expanding Green’s function e i k | r ′ − r | / | r ′ − r | {e^{ik\left | {r’ - r} \right |}}/\left | {r’ - r} \right | in the cylindrical coordinate system; (2) transforming Green’s function e i k | r ′ − r | / | r ′ − r | {e^{ik\left | {r’ - r} \right |}}/\left | {r’ - r} \right | into Green’s function 1 / | r ′ − r | 1/\left | {r’ - r} \right | by setting the wave number k k to be zero and integrating the separated azimuthal function cos n ( ϕ ′ − ϕ ) {\cos ^n}\left ( {\phi ’ - \phi } \right ) ; (3) using the integral r
Source: Quarterly of Applied Mathematics
DOI: 10.1090/qam/1096238
Author: Wan-xian Wang
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2479399047