The purpose of this note is to quantitatively study the asymptotic beh
avior of the dipole magnetic field in the tail region of a paraboloida
l or cylindrical model of the magnetosphere, assuming the complete scr
eening of the internal field by magnetopause currents. This screening
assumption is equivalent to imposing the boundary condition that the n
ormal component of the magnetic field is zero at the magnetopause. Wit
h this boundary condition, the screened dipole field falls off exponen
tially with distance down the tail, in sharp contrast to the bare dipo
le field. Analytic expressions for a cylindrical and paraboloidal magn
etopause are given.