电介质中的偶极子：远距离电场的有趣结果和形状依赖性
A dipole in a dielectric: Intriguing results and shape dependence of the distant electric field
摘要：
将点电偶极子置于介质中半径为$R$的球形空腔的中心，然后让$R\to 0$。这一结果与教科书中的基本答案不一致。数学和物理原因的分歧进行了讨论。这种差异是由相同的限制程序适用于一个均匀极化的球体嵌入在电介质中确认。接下来，我们解决了同样的问题，一个极化的球体沉浸在一个无限的电介质，并发现，渐近电位显示出意想不到的形状依赖性，即使在一个任意小的球体的限制。通过考虑扁长球和长椭球，并采取适当的限制，我们恢复的基本教科书的答案或以前的结果发现的极化球。
英文摘要：
The field of a point electric dipole in an infinite dielectric is obtained by placing the dipole at the center of a spherical cavity of radius $R$ inside the dielectric and then letting $R\to 0$. The result disagrees with the elementary answer found in textbooks. The mathematical and physical reasons for the disagreement are discussed. The discrepancy is confirmed by the same limiting procedure applied to a uniformly polarized sphere embedded in the dielectric. We next solve the same problem for a polarized spheroid immersed in an infinite dielectric and find that the asymptotic potential shows an unexpected shape dependence, even after taking the limit of an arbitrarily small spheroid. By considering both oblate and prolate spheroids and taking appropriate limits, we recover either the elementary textbook answer or the previous result found for the polarized sphere.
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