There has been a significant controversy over the past decade regarding the relative information content of bioelectric and biomagnetic signals. In this paper we present a new, theoretical example of an electrically-silent magnetic field, based on a bidomain model of a cylindrical strand of tissue generalized to include off-diagonal components in the conductivity tensors. The physical interpretation of the off-diagonal components is explained, and analytic expressions for the electrical potential and the magnetic field are found. These expressions show that information not obtainable from electrical potential measurements can be obtained from measurements of the magnetic field in systems with conductivity tensors more complicated than those previously examined. © 1986 Biophysical Society.