We discuss the physical conditions that determine the configuration of the polar cusps in earth's magnetosphere. In the conventional picture, the cusp-associated neutral points lie on the dayside magnetopause. An alternative picture has been suggested by C. -C. Wu on the basis of his global magnetohydrodynamic (MHD) simulation: the polar cusps are swept back away from the sun, so that the magnetopause neutral points lie on the nightside of the earth. On the basis of two-dimensional linear equilibrium calculations, we believe that the amount of plasma (i.e., the magnitude of the thermal plasma pressure) on low-latitude polar cusp field lines is the most influential parameter that determines the cusp configuration: when the plasma pressure varies between zero (vacuum case) and the Harris sheet limit (zero Bz in the tail plasma sheet), the standard cusp geometry results with the two neutral points on the dayside magnetopause. When the plasma pressure exceeds the Harris sheet limit, the cusp field lines gradually shift to the nightside, until the neutral points are located tailward of the dipole. We considered three possible plasma supply mechanisms for polar cusp field lines: (1) Observed energetic ions flowing up from the ionosphere are shown to be clearly inadequate to create a Wu-type cusp. (2) Adiabatic sunward drift of plasma sheet or ring current plasma from the nightside to the dayside is also clearly insufficient. (3) Particle diffusion through the dayside magnetopause could create only a thin layer of plasma on closed field lines, where the pressure might be sufficient to create a Wu-type cusp. We suspect that unrealistically large numerical-diffusion coefficients could cause MHD codes to predict unrealistically prominent closed-field-line boundary layers and corresponding Wu-type cusp configurations.