We study the electric potential of a charge placed in a strong magnetic field $B\gg B_0\simeq 4.4\times {10}^{13}\mathrm{G}$, as modified by the vacuum polarization. In such a 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 the Yukawa law. The electromagnetic interaction regains its long-range character at distances larger than the Compton length, the potential decreasing across $\mathbf{B}$ faster than along. Correction to the nonrelativistic ground-state energy of a hydrogenlike atom is found. In the limit $B=\infty$, 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.

• Received 24 July 2006

DOI:https://doi.org/10.1103/PhysRevLett.98.180403