is for a current of (A) and a loop of radius . Close to the loop, the magnetic field at a distance along the center-line axis perpendicular to the loop is derived from the Biot–Savart law in Section 5-2, equation (25) as follows. At a distance far from the loop center the magnetic field is approximately that produced by a magnetic dipole. Since the pressure at the magnetospheric boundary is doubled due to compression of the magnetic field and is the following at a point along the center-line axis at a distance for the target magnetopause standoff distance from equation (5). Equating this to the dynamic pressure for a plasma environment , inserting from equation and solving for yields equation (6). Andrews and Zubrin derived equation (8) for the drag force of the sail that determined the characteristic length for a tilt angle but according to Section 6.5 of Freeland an error was made in numerical integration in choosing the ellipse downstream from the magnetopause instead of the ellipse upstream that made those results optimistic by a factor of approximately 3.1, which should be used to correct any drag force results using equation (8). Instead, this article uses the approximation from equation (108) for a spherical bubble that corrects this error and is close to the analytical formula for the axial configuration as the force for the Magsail as follows In 2004 Toivanen and Janhunen did further analysis on the Magsail that they called a Plasma Free MagnetoPause (PFMP) that produced similar results to that of Andrews and Zubrin. Coil mass and current (CMC) The minimum required mass to carry the current in equation or other magnetic sail designs is defined in equation (9) and equation (3) as follows: where (A/m2) is the superconductor critical current density and (kg/m3) is the coil material density, for example 6,500 for a superconductor. The physical mass of the coil is where (m) is the radius of the superconductor wire, for example that necessary to handle the tension for a particular use case, with the factor (e.g., 3) accounting for mass of the tether (or shroud) lines. Note that with =0 must be no less than in order for the coil to carry the current . Setting equation with =0 equal to equation and solving for yields the minimum required coil radius If operated within the solar system, high temperature superconducting wire (HTS) is