Is the Earth's Magnetic Field a Constant? A Legacy of Poisson

In the report he submitted to the Academie des Sciences, Poisson imagined a set of concentric spheres at the origin of Earth's magnetic field. It may come as a surprise to many that Poisson as well as Gauss both considered the magnetic field to be constant. We propose in this study to test this surprising assertion for the first time, evoked by Poisson in 1826. First, we present a development of Maxwell's equations in the framework of a static electric field and a static magnetic field in order to draw the necessary consequences for the Poisson hypothesis. In a second step, we see if the observations can be in agreement with Poisson. To do so, we choose to compare (1) the polar motion drift and the secular variation of Earth's magnetic field, (2) the seasonal pseudo-cycles of day length together with those of the sea level recorded by different tide gauges around the globe and those of Earth's magnetic field recorded in different magnetic observatories. We then propose a mechanism, in the spirit of Poisson, to explain the presence of the 11-year cycle in the magnetic field. We test this mechanism with observations, and finally, we study closely the evolution of the g(1,0) coefficient of the International Geomagnetic Reference Field (IGRF) over time.