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.

• Received 15 October 2012

DOI:https://doi.org/10.1103/PhysRevD.86.125028