Halliday, Resnick & Walker — Maxwell's Equations; Magnetism of Matter: Problem 15

15 The magnitude of the magnetic dipole moment of Earth is \(8.0 \times 10^{22} \text{ J/T}\). (a) If the origin of this magnetism were a magnetized iron sphere at the center of Earth, what would be its radius? (b) What fraction of the volume of Earth would such a sphere occupy? Assume complete alignment of the dipoles. The density of Earth’s inner core is \(14 \text{ g/cm}^3\). The magnetic dipole moment of an iron atom is \(2.1 \times 10^{-23} \text{ J/T}\). (Note: Earth’s inner core is in fact thought to be in both liquid and solid forms and partly iron, but a permanent magnet as the source of Earth’s magnetism has been ruled out by several considerations. For one, the temperature is certainly above the Curie point.)