We present a 2-D potential-field model for the magnetic structure in t
he environment of a typical quiescent polar-crown prominence. The fiel
d is computed using the general method of Titov (1992) in which a curv
ed current sheet, representing the prominence, is supported in equilib
rium by upwardly directed Lorentz forces to balance the prominence wei
ght. The mass density of the prominence sheet is computed in this solu
tion using a simple force balance and observed values of the photosphe
ric and prominence magnetic field. This calculation gives a mass densi
ty of the correct order of magnitude. The prominence sheet is surround
ed by an inverse-polarity held configuration adjacent to a region of v
ertical, open polar field in agreement with observations. A perturbati
on analysis provides a method for studying the evolution of the curren
t sheet as the parameters of the system are varied together with an ex
amination of the splitting of an X-type neutral point into a current s
heet.