There are suggestions in the electrochemical literature that a body force F-Delta c acts when an electrolyte with a non-uniform concentration c of paramagnetic ions is subject to a uniform magnetic field. We demonstrate, experimentally and theoretically, that no such magnetic body force exists, to first order. A second-order correction associated with the demagnetizing field does lead to a very small concentration-dependent body force, which is not expected to produce any observable effect in electrochemistry.