Conditions for the appearance of "bald patches" at the solar surface

A general criterion for the existence of sections of the photospheric polarity inversion line where the overlying magnetic field lines are parallel to the photosphere is presented. It is shown that such sections, called "bald patches", exist for a wide range of parameters in potential and constant-α force-free fields created by four concentrated sources of magnetic flux. Bald patches appear when the polarity inversion line is bent too much in an S-like manner. The appearance of bald patches may be important for the formation of prominences and possibly for solar flares.