Dependence of the amount of open magnetic flux on the direction of the interplanetary magnetic field

The power generated by the solar wind—magnetosphere dynamo is proportional to the amount of the open magnetic flux Φ. It is difficult to use this fact in determining observationally the dependence of Φ on the orientation of the interplanetary magnetic field vector. It is shown that, for a simple vacuum superposition of the earth's dipole field and a uniform magnetic field, Φ is very closely proportional to sin θ/2) for a wide range of the intensity of the uniform field, where θ denotes the polar angle of the interplanetary magnetic field vector in the Y-Z plane of solar-magnetospheric coordinates.