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**Multi-dimensional inhomogeneity indicators and the force on uncharged spheres in electric fields.**
*(English)*
Zbl 1160.35388

Summary: Uncharged droplets on outdoor high-voltage equipment suffer a non-vanishing total force in non-homogeneous electric fields. Here, the model problem of a spherical test body is considered in arbitrary dimensions. A series expansion of inhomogeneity indicators is proven, which approximates the total force in local terms of the undisturbed electric field. The proof uses the ideas of generalized spherical harmonics without referring to the particular choice of the orthonormal system. The fast converging series expansion establishes a relationship between the solutions of two partial differential equations on different domains.

### MSC:

35J25 | Boundary value problems for second-order elliptic equations |

65Z05 | Applications to the sciences |

78A25 | Electromagnetic theory (general) |

42B99 | Harmonic analysis in several variables |

33C90 | Applications of hypergeometric functions |

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\textit{D. Langemann}, Math. Methods Appl. Sci. 32, No. 7, 798--810 (2009; Zbl 1160.35388)

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