  We study electric potential of a charge placed in a strong magnetic field
B>>4.4x10^{13}G, as modified by the vacuum polarization. In such field the
electron Larmour radius is much less than its Compton length. At the Larmour
distances a scaling law occurs, with the potential determined by a
magnetic-field-independent function. The scaling regime implies short-range
interaction, expressed by Yukawa law. The electromagnetic interaction regains
its long-range character at distances larger than the Compton length, the
potential decreasing across the magnetic field faster than along. Correction to
the nonrelativistic ground-state energy of a hydrogenlike atom is found. In the
infinite-magnetic-field limit the modified potential becomes the Dirac
delta-function plus a regular background. With this potential the ground-state
energy is finite - the best pronounced effect of the vacuum polarization.

Astrophysics;High Energy Physics - Theory;Atomic Physics