  It is shown that the covariance of Lagrangians always taking place results in
a distortion of any electric and magnetic fields by a pseudoscalar field of
axions and axion-like particles. As a result, electric and magnetic fields
acquire oscillating magnetic and electric components, respectively. One can
also use the equivalent approach based on an introduction of effective
oscillating magnetic charges and electric dipole moments in undistorted
electromagnetic fields. The determined relations between the magnetic charges
and electric dipole moments and the axion-photon coupling constant open a
possibility to compare a sensitivity of search for axions in optical
experiments and experiments with massive particles. The inverse (dual) Witten
effect defining effective magnetic charges of electrically charged particles
opens new exciting possibilities to search for axions and axion-like particles
with very small masses in nonresonance experiments. The study of a passage of
strongly decelerated electrons or positrons through a solenoid is proposed.
