The near earth magnetic field of the magnetotail current

In the forward part of the magnetosphere the distant tail current system approximates a magnetic quadrupole composed of two distorted adjacent solenoids. The current in the neutral sheet at this distance is accurately approximated as an infinitesimally thin current sheet. We have calculated the magnetic field near the Earth by integrating over the entire tail current system assuming the magnetotail is a cylinder of constant radius and that the tail current decreases with distance into the tail as $\text{|x|}{}^{\mathrm{<mtext>?1</mtext><mtext>3</mtext>}}$. The field is then represented by a scalar potential expanded into spherical harmonics which may be conveniently added to the spherical harmonic expansion of the scalar potential representing the magnetopause current system.