A general criterion for the existence of sections of the photospheric
polarity inversion line where the overlying magnetic field lines are p
arallel to the photosphere is presented. It is shown that such section
s, called ''bald patches'', exist for a wide range of parameters in po
tential and constant-alpha force-free fields created by four concentra
ted sources of magnetic flux. Bald patches appear when the polarity in
version line is bent too much in an S-like manner. The appearance of b
ald patches may be important for the formation of prominences and poss
ibly for solar flares.