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- W2020392013 abstract "The classical treatment of the Laplace equation by electrical inversion is used to obtain analytical expressions for the two-dimensional perturbed electrostatic fields in the presence of a two-phase 2D object. The geometry of the two-phase object is composed of two overlapping infinitely long cylinders Ca and Cb of radii a and b, respectively, intersecting at a vertex angle . The composite inclusion has the shape resembling a 2D snowman type of object with a conducting cylinder Ca partly protruded into the dielectric cylinder Cb with a dielectric constant different from that of the host medium. The mathematical problem with this inclusion in the electrostatic environment is formulated in terms of electric potentials (and complex potentials as well) with the mixed Dirichlet and Neumann boundary conditions at the boundary of the hybrid object. General expressions for the perturbed electrostatic fields in the two phases are obtained in a straightforward fashion using Kelvin's inversion together with shift and reflection properties of harmonic functions. The general results are exploited to derive solutions for the hybrid object embedded in (i) a transverse or a longitudinal uniform field and (ii) a field generated by a dipole. The dipole coefficients are extracted directly from the exact solutions in a fairly simple manner. The plots of the normalized polarizabilities (derived from dipole coefficients) for the imposed uniform field show that the polarizability in the longitudinal direction is greater or less than the transverse polarizability depending on the dielectric constants of the composite body and the host medium. The equipotential plots generated using the exact solutions also show fascinating field patterns. An interesting connection between the present solutions and the cyclic groups in abstract algebra is outlined as well in the appendix." @default.
- W2020392013 created "2016-06-24" @default.
- W2020392013 creator A5091725643 @default.
- W2020392013 date "2005-06-22" @default.
- W2020392013 modified "2023-10-04" @default.
- W2020392013 title "Classical image treatment of a geometry composed of a circular conductor partially merged in a dielectric cylinder and related problems in electrostatics" @default.
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- W2020392013 doi "https://doi.org/10.1088/0305-4470/38/27/011" @default.
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