SIMULATION OF THE ELECTROSTATIC DIPOLE FIELD IN THE PRESENCE OF A THIN UNCLOSED OBLATE ELLIPSOIDAL SHELL AND PLANE - G. Ch. Shushkevich (Informatika, 2017)
An analytical solution of axially symmetric problem for determining the field of an electrostatic dipole located inside a thin unclosed oblate ellipsoidal shell in the presence of a grounded plane is constructed. Using the addition theorems connecting spherical, ellipsoidal and cylindrical harmonic functions, the solution of the boundary problem is reduced to the solution of dual series equations by the Legendre polynomials that are transformed to an infinite system of linear algebraic equations of the second kind with a completely continuous operator. The influence of the geometrical parameters of the problem on the value of the secondary potential of the electrostatic field is numerically investigated, the corresponding graphs are given.