It is known that observers comoving with a uniformly accelerated point charge detect the electromagnetic field of a charge as a static electric field. We show that one can find a similar family of observers, which detect the field of a charge as a static electric field, in the general case of arbitrary point-charge motion. We find the velocities of these observers and the conditions under which such observers exist. This paper is aimed at graduate students and specialists. (Contains 3 footnotes and 2 figures.)