A simple model of the interplanetary magnetic field is described and solved analytically. In this model space is divided into three regions by two concentric spheres. Conductivities (with one exception) are assumed to be isotropic and constant in each region, and flow velocities are regular and prescribed. The innermost region rotates rigidly around its center, the intermediate region contains a compressible fluid flowing radially outward at a constant velocity (an idealization of the solar wind), and the outer region is at rest. The magnetic field originates at point sources at the origin and possibly in a uniform field at infinity. With these assumptions methods are described for finding the field in the general case, and also in the limit when all conductivities are very high. As an example the case in which the field's source is a point dipole aligned with the axis of rotation is solved in some detail. Part II of this study, published as a separate Technical Note, considers the cosmic ray anisotropy.
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