Relativistic Paradox of a Uniformly Charged Sphere Moving with Constant Velocity

A magneto-electric field appearing in a laboratory due to moving charges has unusual properties. In particular, such a field of kinematical origin does not obey the wave equation with a non-relativistic velocity instead of light speed; so, its movement resembles that of a rigid body. In this paper the field of a uniformly charged sphere moving at constant velocity is considered. Relativistic axiom, implicitly used in the derivation of formulas describing a kinematic deformation for the proper spherical field from the point of view of a fixed observer, is revealed. A discrepancy was found between the generally accepted idea of the configuration of a deformed field and its real geometry. It is shown that the correct interpretation of known formulas leads to a logical contradiction, which cannot be eliminated within the framework of the theory of relativity. A scheme of a decisive experiment is proposed.