As an example in magnetostatics we consider the main magnetic field of the Earth and its current sources. The measured field on the surface is accurately given, in tables of the International Geological Reference Field, in terms of Gaussian coefficients. By applying Maxwell’s equations to these data we calculate the extended field, inside the Earth, and give graphical representations of it. We also construct a simple theoretical model of the source of the field, in which the field is the result of currents flowing on the surface of a sphere inside the Earth. The current sources which give the observed field are calculated in terms of vector spherical harmonics. The stream function and currents are displayed on a Mercator projection for a sphere whose radius is half the Earth’s radius. Interesting properties of vector operations on the Mercator plane are analytically and graphically described.

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