Theory of Perturbation of Electrostatic Field By A Coated Anisotropic Dielectric Sphere.

This article focuses on the analytical formulation and solution of the perturbation of an electrostatic field by a coated dielectric sphere composed of two distinct linear anisotropic dielectric (LAD) materials. Using specific affine transformations, the authors represent the electric potential inside both the core and coating in terms of Laplace equation solutions and derive a transition matrix relating the source potential to the perturbation potential in the exterior region. The formulation accommodates arbitrary anisotropy and biaxiality in the core and coating materials, including their relative orientation via rotation dyadics, and can be extended to multilayered spheres. Numerical results illustrate how anisotropy, coating presence, core radius, and relative rotation affect the internal and perturbation potentials for point-charge and point-dipole sources, highlighting that the rotation of anisotropic layers has a more pronounced effect as the core radius approaches the outer radius. The study provides a foundational method for electrostatic analysis of anisotropic core–shell particles relevant to applications in drug delivery, biomedical imaging, and catalysis.