Measurements of the DC electrical potential near the top of Earth's mantle have been extrapolated into the deep mantle in order to estimate the strength of the toroidal magnetic field component at the core-mantle interface. Recent measurements have been interpreted as indicating that at the core-mantle interface, the magnetic toroidal and poloidal field components are approximately equal in magnitude. A motivation for such measurements is to obtain an estimate of the strength of the toroidal magnetic field in the core, a quantity important to our understanding of the geomagnetic field's dynamo generation. Through the use of several simple and idealized calculations, this paper discusses the theoretical relationship between the amplitude of the toroidal magnetic field at the core-mantle boundary and the actual amplitude within the core. Under physical conditions believed to characterize the core and mantle a low value of the field at the core-mantle boundary is an inevitable consequence of the electrical conductivity contrast between core and lower mantle material; this conclusion is largely independent of details of the mantle's conductivity profile. Sample calculations, based on simplifying assumptions, are also used to explore the extrapolation of the toroidal field amplitude into the core. Even with a very low inferred value of the toroidal field amplitude at the core-mantle boundary (~ few gauss), the toroidal field amplitude within the core could be consistent with a magnetohydrodynamic dynamo dominated by nonuniform rotation and having a strong toroidal magnetic field. ¿ American Geophysical Union 1991