  Nonlinear Maxwell equations are written up to the third-power deviations from
a constant-field background, valid within any local nonlinear electrodynamics
including QED with a Euler-Heisenberg (EH) effective Lagrangian. The linear
electric response to an imposed static finite-sized charge is found in the
vacuum filled by an arbitrary combination of constant and homogeneous electric
and magnetic fields. The modified Coulomb field and corrections to the total
charge and to the charge density are given in terms of derivatives of the
effective Lagrangian with respect to the field invariants. These are
specialized for the EH Lagrangian.
