Although the electromagnetic field of a given distribution of charge and current is unambiguously
defined by the Maxwell equations, there is no unique inverse correspondence between this field and
point-like sources. We prove this statement for electric and magnetic dipoles and discuss two
examples when the same field at some point or in some region is generated by either a dipole or an
electric charge that are varying in different ways. The electric and magnetic fields of the charge
depend on its speed and the distance between the charge and the observation point. It is shown that
it is possible to find a law of motion for the charge in which the variation in the distance to the
observer is compensated for by variation in the velocity of the charge. One particular example of
the motion of a charge is discussed, wherein the electric and magnetic fields at a specific point of
observation remain constant. The issues discussed could be of interest to both scientists and
scholars.