Study on the Boundary Value Problem of Laplace's Equation in a Cylindrical Cavity with Sector-Shaped Cross-Section

This paper presents an analytical solution to the boundary value problem of Laplace’s equation in a cylindrical cavity with a sector-shaped cross-section. The solution is derived using the method of separation of variables in cylindrical coordinates, combined with the superposition principle for boundary conditions. The results agree well with those from commercial simulation software, confirming the accuracy and reliability of the approach. The study also introduces modified Bessel functions of imaginary order and their properties, offering insights relevant to similar problems. This work provides a novel analytical framework for complex geometries in electromagnetic field analysis and demonstrates potential for engineering applications.