A curious property of the electrostatic image theory for the perfectly conducting prolate spheroid, introduced in 2001, is pointed out: the potential outside the conducting spheroid remains unchanged if the conductor is replaced by a dielectric spheroid with an embedded charge which coincides with the image charge for the conducting spheroid case. The present note is a generalization of the corresponding observation about the classical Kelvin image theory for the conducting sphere, made in 1988.

An interesting property of the magnetostatic image theory for a superconducting sphere in the field of a static circular current loop with its axis radial to the sphere is pointed out: the magnetic field outside the superconducting sphere remains unchanged if the superconductor is replaced by a permeable sphere with an embedded current loop which coincides with the image current for the superconducting sphere case. An alternative path for reaching the conclusion is proposed as an exercise for the student.