Analytical Estimation of the Scale of Earth-Like Planetary Magnetic Fields

In this paper we analytically estimate the magnetic field scale of planets with physical core conditions similar to that of Earth from a statistical physics point of view. We evaluate the magnetic field on the basis of the physical parameters of the center of the planet, such as density, temperature, and core size. We look at the contribution of the Seebeck effect on the magnetic field, showing that a thermally induced electrical current can exist in a rotating fluid sphere. We apply our calculations to Earth, where the currents would be driven by the temperature difference at the outer-inner core boundary, Jupiter and the Jupiter’s satellite Ganymede. In each case we show that the thermal generation of currents leads to a magnetic field scale comparable to the observed fields of the considered celestial bodies.