The presence of anisotropic plasma distributions, trapped at the Earth's magnetic equator, has consequences for the electric field structure which must exist in equilibrium along the magnetic field line. Data from SCATHA and Dynamics Explorer 1 indicate that the core ion distributions at the magnetic equator can be well described as bi-Maxwellian distributions, with a perpendicular temperature an order of magnitude larger than the parallel temperature. A collisionless model is developed for the variation in plasma parameters, following the forms developed by Whipple (1977). If the core electron anisotropy is low, the resulting electric field of ~0.1 &mgr;V m-1 is pointed away from the equator. Under these conditions the self-consistent electric field will not overcome the effects of magnetic trapping. The resulting potential distribution results in a local maximum in total plasma density at the equator. Only when the electron distribution is primarily field-aligned can there be a density minimum at the equator. Comparisons are made between this model and the observed variations in DE 1 plasma parameters with latitude.