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Suppose that the magnetic dipole moment of Earth is 6.4 × 1020 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? The radius of Earth is 6.37 x 106 m. Assume complete alignment of the dipoles. The density of Earth's inner core is 15 g/cm³. The magnetic dipole moment of an iron atom is 2.1 x 10-23 J/T. Iron has a molar mass of 55.9 g/mol. (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.)

Suppose that the magnetic dipole moment of Earth is 6.4 × 1020 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? The radius of Earth is 6.37 x 106 m. Assume complete alignment of the dipoles. The density of Earth's inner core is 15 g/cm³. The magnetic dipole moment of an iron atom is 2.1 x 10-23 J/T. Iron has a molar mass of 55.9 g/mol. (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.)

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Suppose that the magnetic dipole moment of Earth is \(6.4 \times 10^{20}\) 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? The radius of Earth is \(6.37 \times 10^6\) m. Assume complete alignment of the dipoles. The density of Earth's inner core is 15 g/cm\(^3\). The magnetic dipole moment of an iron atom is \(2.1 \times 10^{-23}\) J/T. Iron has a molar mass of 55.9 g/mol. (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.) - **(a) Number:** 0.17 - **Units:** degrees - **(b) Number:** 1.0e21 - **Units:** degrees **Explanation:** This text presents a problem regarding the Earth's magnetic dipole moment, asking for calculations related to a hypothetical iron sphere at Earth's center and ensuring considerations about Earth's actual inner core state are mentioned. The provided inputs are placeholders with units of degrees, likely needing revision for correctness in scientific contexts.
Transcribed Image Text:Suppose that the magnetic dipole moment of Earth is \(6.4 \times 10^{20}\) 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? The radius of Earth is \(6.37 \times 10^6\) m. Assume complete alignment of the dipoles. The density of Earth's inner core is 15 g/cm\(^3\). The magnetic dipole moment of an iron atom is \(2.1 \times 10^{-23}\) J/T. Iron has a molar mass of 55.9 g/mol. (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.) - **(a) Number:** 0.17 - **Units:** degrees - **(b) Number:** 1.0e21 - **Units:** degrees **Explanation:** This text presents a problem regarding the Earth's magnetic dipole moment, asking for calculations related to a hypothetical iron sphere at Earth's center and ensuring considerations about Earth's actual inner core state are mentioned. The provided inputs are placeholders with units of degrees, likely needing revision for correctness in scientific contexts.
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