Does a Curved Mirror Honestly Reflect Your Identity? A Study of Multipole Images in Front of a Grounded Sphere

Abstract

The method of image charges is a powerful and elegant technique in electrostatics, commonly used to determine the electric field generated by point charges near conductors of various shapes. While standard problems focus on single charges interacting with conductors, the behavior of multipoles in such configurations has received comparatively less attention, particularly beyond the well-studied case of a flat plane. In this paper, we explore the image formation of electric dipoles and quadrupoles near a conducting sphere and uncover a wonderful result: the image of a given multipole is not necessarily of the same type. Instead, alongside the expected multipole image, the resulting image configuration also includes lower-order multipole contributions. This finding broadens the understanding of electrostatic images and offers new insights into the interaction of multipoles with conducting boundaries.