在静电场和静磁场的平均上，偶极场和退极化场的奇异性
On the average of electrostatic and magnetostatic fields, the singularities of dipole fields and depolarizing fields
摘要：
在“经典电动力学”（杰克逊）的一个定理证明了一个平均的静电场或静磁场在一个球形体积。该定理的证明是基于球谐函数的展开式，它对于导出偶极场的奇异性是有用的。在本文中，我们给这个定理的一个简单的证明，关键元素是使用互易性。该方法还突出了偶极子奇异性和球的去极化场之间的关系，因此也很容易找到。此外，这一联系使我们能够将定理推广到更一般的椭球体积。不幸的是，我们只能用这种方法证明去极化张量的存在，还需要另一种方法来实际计算张量。最后将理论推广到各向异性背景介质。
英文摘要：
In "Classical Electrodynamics" (Jackson) a theorem is proved on the average of an electrostatic or magnetostatic field over a spherical volume. The proof of the theorem is based on an expansion in spherical harmonics and it is useful for deriving the singular behaviour of dipole fields. In this paper we give a simple proof of this theorem, the key element being to use reciprocity. The method also highlights the relation between the dipole singularity and the depolarizing field of a sphere, which is thus also found very easily. In addition this link enables us to extend the theorem to a more general ellipsoidal volume. Unfortunately one can only prove the existence of the depolarizing tensor in this way and one still needs another method for actually calculating the tensor. Finally the theory is also extended to an anisotropic background medium.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
