Modeling the kinematic magnetic field in the solar wind beyond the terminal shock shows that a ridge of magnetic pressure is produced just inside the heliopause. This ridge has its maximum amplitude in the plane defined by the solar rotation axis and the heliotail and decreases to zero amplitude in the solar equatorial plane. The ridge is sufficiently large that it will cause the layer immediately inside the heliopause to thicken, pushing the heliopause outward and slightly affecting its position relative to the terminal shock. However, the ridge is far too thin to cause an important change in the distance of the terminal shock from the Sun. The kinematic assumption prevents us from estimating the actual magnitude of the ridge, but we show that these conclusions are a simple consequence of geometrical arguments for incompressible, steady, laminar flows. Moreover, the heliopause magnetic field originates on the terminal shock near the substagnation point. Consequently, the heliospheric current sheet field reversals are painted onto the inside surface of the heliopause. Alternate magnetic polarity strips will be oppositely directed relative to the interstellar magnetic field, implying that reconnection inevitably occurs on a fine scale near the nose of the heliosphere. This suggests that the heliopause is a leaky, diffuse surface. ¿ American Geophysical Union 1993