A boundary-value problem for dielectric spherical void in a homogeneous insulator by considering surface conductivity

In this paper, the boundary-value problem satisfying the Dirichlet condition has been solved for the case of a dielectric, spherical void inside a homogeneous insulator by considering surface conductivity. Mathematical equations have been derived to calculate the respective electric fields E_i(t)and E_e(t) inside and outside spherical gas voids that exist within an insulator by considering the surface conductivity γ_s of gas voids having an electric permittivity of ε_i and conductivity γ_i under DC (ωτ?1) and AC (ωτ?1) conditions. The expression for the dipole moment of a polarized spherical dielectric particle has been obtained in accordance with the determined electric field E_i(t). The derived expressions are then applied to calculate reciprocal interaction force between the spherical particle and metallic electrodes, which is very considerable for the dielectric separation processes in the DC and AC cases.