A candidate mechanism for the interaction of magnetic fields with living systems
Some biological molecules can be split into two free radicals - reactive species with single, unpaired electrons and therefore a spin. Whether they recombine or stay separate depends on whether the two spins change direction or not. A magnetic field can change the spins. So this is a mechanism whereby magnetic fields can affect the outcome of a chemical reaction and change the concentrations of these reactive species.
For this to happen, there has to be the right combination of conditions: the recombination time, the strength of the external magnetic field compared to internal magnetic fields, and so on. The effect has been demonstrated many times at relatively high fields, a mT or more. But it hasn't yet been demonstrated at the lower fields, of order a microtesla, implicated by the epidemiology. Research continues (including by the EMF Biological Research Trust, which has pioneered this area), but free radicals can not yet be regarded as a plausible mechanism.
There is also another reason why it seems that this mechanism cannot underlie the epidemiological results. Free-radical reactions typically have timescales of tens of nanoseconds, compared to which 50 Hz fields are effectively static. The relevant magnetic field is therefore the instantaneous total field, which is usually dominated not by the power-frequency component but by the geomagnetic field, which is around 50 µT in the UK. See more discussion of this issue and a test of one of the implications.