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We find third-power nonlinear corrections to the Coulomb and other staticelectric fields, as well as to the electric and magnetic dipole fields, as wework within QED with no background field. The nonlinear response function webase our consideration on is the fourth-rank polarization tensor, calculatedwithin the local (infrared) approximation of the effective action. Therefore,the results are applicable to weakly varying fields. It is established that thenonlinear correction to magnetic moment of some baryons just matches, in theorder of magnitude, the existing gap between its experimental and theoreticalvalues.

Nonlinear corrections in basic problems of electro- and magneto-statics in the vacuum