Nonlinear (magnetic) correction to the field of a static charge in an external field

We find the first nonlinear correction to the field produced by a static charge at rest in a background constant magnetic field. It is quadratic in the charge and purely magnetic. The third-rank polarization tensor---the nonlinear response function---is written within the local approximation of the effective action in an otherwise model- and approximation-independent way within any $P$-invariant nonlinear electrodynamics, QED included.