Solar flares are frequently observed to occur where new magnetic flux is emerging and pressing up against strong active region magnetic fields. Since the solar plasma is highly conUucting, current sheets develop at the boundary between the emergent and ambient flux, provided the two magnetic fields are inclined at a non-zero angle to one anGther.
The present paper gives a simple two-dimensional model for the development of such sheets under the assumptions that no reconnection occurs and that the surrounding field remains a potential one. By using complex variable techniques, the position, orientation and shape of a current sheet may be determined, as well as the excess magnetic energy associated with it. Two examples are considered. The first, in which the ambient field is bipolar, may model new flux emergence near the edge of an active region, while the second example assumes a constant ambient field and may approximate the so-called 'fibril crossings' which occur prior to some flares. In each case, the current sheets are curved, and the magnetic energy which is stored in excess of potential is sufficient to supply a solar flare when the sheets are long enough.