A mechanism is presented that predicts new biological effects of static and sinusoidal weak magnetic fields. The model is based on an earlier proposed interference mechanism of quantum states of ions within protein cavities. The quantum dynamics of an ion is studied for the case of ion–protein complexes that rotate in magnetic fields. Both the individual molecular rotation and rotation together with a biological sample are taken into account. A formula is derived for the magnetic field‐dependent part of the dissociation probability of an ion–protein in these conditions. The formula explains the unusual amplitude dependence of the known biological effect in PC‐12 cells exposed to AC–DC magnetic field. The dependence had the functional motif J21(2HAC/HDC), where J1 is the first order Bessel function of the first kind. A good fit was obtained assuming individual rotation of the Li–protein complex in MF. The macroscopic rotation of a biological system, even at low speed 1.5–2 Hz, is predicted to reduce the biological effects of a “magnetic vacuum” and to shift the spectral peaks in the field and frequency dependencies of some magnetobiological effects. Bioelectromagnetics 21:34–45, 2000. © 2000 Wiley‐Liss, Inc.