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The properties of the electric field of a two-body system consisting of aReissner-Nordstr\"om black hole and a charged massive particle at rest haverecently been analyzed in the framework of first order perturbation theoryfollowing the standard approach of Regge, Wheeler and Zerilli. In the presentpaper we complete this analysis by numerically constructing and discussing thelines of force of the "effective" electric field of the sole particle with thesubtraction of the dominant contribution of the black hole. We also give thetotal field due to the black hole and the particle. As the black hole becomesextreme an effect analogous to the Meissner effect arises for the electricfield, with the "effective field" lines of the point charge being expelled bythe outer horizon of the black hole. This effect existing at the level of testfield approximation, i.e. by neglecting the backreaction on the backgroundmetric and electromagnetic field due to the particle's mass and charge, is herefound also at the complete perturbative level. We point out analogies withsimilar considerations for magnetic fields by Bi{\v c}\'ak and Dvo{\v r}\'ak.We also explicitly show that the linearization of the recently obtainedBelinski-Alekseev exact solution coincides with our solution in theRegge-Wheeler gauge. Our solution thus represents a "bridge" between the testfield solution, which neglects all the feedback terms, and the exact two-bodysolution, which takes into account all the non-linearity of the interaction.

Charged massive particle at rest in the field of a Reissner-Nordstr\"om black hole. II. Analysis of the field lines and the electric Meissner effect