The expanded variant of the lectures delivered at the 39th ITEP Winter School in 2011
We obtain the following analytical formula which describes the dependence of the electric potential of a point-like charge on the distance away from it in the direction of an external magnetic field B: Phi(z) = e/|z| [ 1- exp(-sqrt{6m_e^2}|z|) + exp(
-sqrt{(2/pi) e^3 B + 6m_e^2} |z|) ]. The deviation from Coulombs law becomes essential for B > 3pi B_{cr}/alpha = 3 pi m_e^2/e^3 approx 6 10^{16} G. In such superstrong fields, electrons are ultra-relativistic except those which occupy the lowest Landau level (LLL) and which have the energy epsilon_0^2 = m_e^2 + p_z^2. The energy spectrum on which LLL splits in the presence of the atomic nucleus is found analytically. For B > 3 pi B_{cr}/alpha, it substantially differs from the one obtained without accounting for the modification of the atomic potential.
