The simple addition of a uniform interplanetary magnetic field and the Earth's dipole magnetic field is used to evaluate electric field convection patterns over the polar caps that result from solar wind flow across open geomagnetic field lines. This model is found to account for observed polar-cap convection patterns as a function of the interplanetary magnetic field components By and Bz. In particular, the model offers an explanation for sunward and antisunward convection over the polar caps for Bz>0. Observed field-aligned current patterns within the polar cap and observed auroral arcs across the polar cap are also explained by the model. In addition, the model gives several predictions concerning the polar cap that should be testable. Effects of solar wind pressure and magnetospheric currents on magnetospheric electric and magnetic fields are neglected. That observed polar cap features are reproduced suggests that the neglected effects do not modify the large-scale topology of magnetospheric electric and magnetic fields along open polar cap field lines. Of course, the neglected effects significantly modify the magnetic geometry, so that the results of this paper are not quantitatively realistic and many details may be incorrect. Nevertheless, the model provides a simple explanation for many qualitative features of polar cap convection.