Abstract: After one century of nuclear physics, the anomalous Rutherford scattering remains a puzzle: its underlying fundamental laws are still missing. The only presently recognized electromagnetic interaction in a nucleus is the so-called Coulomb electric force, in 1/r, only positive thus repulsive in official nuclear physics, explaining the Rutherford scattering at low kinetic energy of the impacting alpha particles. At high kinetic energy the Rutherford scattering formula doesn’t work, thus called “anomalous scattering”. I have discovered that, to solve the problem, it needs only to replace, at high kinetic energy, the Coulomb repulsive electric potential in 1/r, by the also repulsive magnetic Poisson potential in 1/r3. In log-log coordinates, one observes two straight lines of slopes, respectively −2 and −6. They correspond with the −1 and −3 exponents of the only repulsive electric and magnetic interactions, multiplied by 2 due to the cross-sections. Both Rutherford (normal and anomalous) scattering have been calculated electromagnetically. No attractive force needed.