The representation of the magnetopause field (i.e., the field contribution by magnetopause currents) in spherical harmonics are an inappropriate representation in the near earth tail. The truncation of the series expansion at order l = 7 or 8 in the spherical harmonics works very well near the earth (r?10 RE), but very many more terms are needed in the tail and a more appropriate, more rapidly converging expansion must be sought. For the case of the solar wind perpendicularly incident on the earth's dipole, we propose both a cylindrical harmonic expansion of eight terms or alternatively a divergence free function of r, ϑ, and ϕ for the r,ϑ and ϕ components of the field. Both work very well. A more accurate set of spherical harmonic coefficents is also presented for r?10 RE since a fit to fields at larger r, which distorts the representation, is not included as in previous work. The total field is, of course, the field represented in this paper plus the dipole field plus the field contribution of the magnetotail currents (Beard, 1979) and to a lesser extent plus trapped plasma currents, Birkeland currents, and any other currents.