# Dipolar response of an ellipsoidal particle with an anisotropic coating

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**Dipolar response of an ellipsoidal particle with an anisotropic coating.** / Ambjörnsson, T; Mukhopadhyay, G.

Research output: Contribution to journal › Article

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*Journal of Physics A: Mathematical and General*, vol. 36, no. 42, pp. 10651-10665. https://doi.org/10.1088/0305-4470/36/42/016

### APA

*Journal of Physics A: Mathematical and General*,

*36*(42), 10651-10665. https://doi.org/10.1088/0305-4470/36/42/016

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*Journal of Physics A: Mathematical and General*. 2003, 36(42). 10651-10665. https://doi.org/10.1088/0305-4470/36/42/016

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### RIS

TY - JOUR

T1 - Dipolar response of an ellipsoidal particle with an anisotropic coating

AU - Ambjörnsson, T

AU - Mukhopadhyay, G

PY - 2003/10/24

Y1 - 2003/10/24

N2 - In this paper we study the response of an ellipsoidal particle with a dielectrically anisotropic coating (the coating dielectric function being different parallel and perpendicular to the coating normal) placed in a constant external electric field. For the coating region we find that potential can be written in terms of solutions to a one-dimensional Heun's equation which is derived from the three-dimensional Gauss equation for the potential in ellipsoidal coordinates. We give solutions to Heun's equation in three forms: for the general case we obtain solutions in terms of a series expansion. For the case of spheroidal particles we write the solutions using hypergeometric functions. For large coating anisotropy we derive a simple form of the solution for the potential. The inside of the ellipsoid and the surroundings are assumed dielectrically isotropic and the potential is therefore given by standard results. By matching the solutions across the boundaries we obtain the ellipsoidal particle polarizability, which is written in terms of the standard depolarization factors and logarithmic derivatives of the Heun's equation solutions. The results above also allow us to obtain the magnetic polarizability of a coated ellipsoid in a constant external magnetic field.

AB - In this paper we study the response of an ellipsoidal particle with a dielectrically anisotropic coating (the coating dielectric function being different parallel and perpendicular to the coating normal) placed in a constant external electric field. For the coating region we find that potential can be written in terms of solutions to a one-dimensional Heun's equation which is derived from the three-dimensional Gauss equation for the potential in ellipsoidal coordinates. We give solutions to Heun's equation in three forms: for the general case we obtain solutions in terms of a series expansion. For the case of spheroidal particles we write the solutions using hypergeometric functions. For large coating anisotropy we derive a simple form of the solution for the potential. The inside of the ellipsoid and the surroundings are assumed dielectrically isotropic and the potential is therefore given by standard results. By matching the solutions across the boundaries we obtain the ellipsoidal particle polarizability, which is written in terms of the standard depolarization factors and logarithmic derivatives of the Heun's equation solutions. The results above also allow us to obtain the magnetic polarizability of a coated ellipsoid in a constant external magnetic field.

U2 - 10.1088/0305-4470/36/42/016

DO - 10.1088/0305-4470/36/42/016

M3 - Article

VL - 36

SP - 10651

EP - 10665

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 42

ER -