This paper provides a broad overview of the physics of magnetism and magnetic fields, tracing key concepts from basic field theory to advanced geophysical phenomena. It covers the relationship between electric and magnetic fields, the Lorentz force, and Faraday's law of electromagnetic induction. The paper also examines how the Earth's magnetic field is generated and maintained through fluid motion in the outer core, the Alpha and Omega effects, and geomagnetic field reversals. Additional topics include Laplace's equation as a tool for mapping electric potential, the discovery of diamagnetism, and speculative future applications of magnetic forces — including levitation and energy generation.
Magnets and magnetism literally help the world go round, and these fundamental forces have provided the source for countless innovations that have improved the standard of living for people around the globe. Magnetic field lines are a way to visualize the field a magnet produces; magnets produce vector fields at all points in the space around them. This field can be defined by measuring the force it exerts on a moving charged particle, such as an electron.
The physics of magnetism requires an understanding of the concept of an electric field. There is a fundamental relation between the force on a charge q in an electric field: F = qE. A magnetic field is the result of a cross product between two vectors. For example, two such vectors lying in the plane of this page with an angle between them produce a resultant field perpendicular to both, as illustrated in Figure 1 below.
Figure 1. The Magnetic Field [Source: University Physics Department].
These calculations become important when considering reversals in the Earth's magnetic field, which were first described by Walter Elsasser and Sir Edward Bullard during the mid-20th century. Today, the general principles governing the regeneration of magnetic fields are well established and represent an apparently common phenomenon throughout the universe.
There are two fundamental processes involved in maintaining the Earth's magnetic field. The first process involves the creation of new magnetic fields from the ambient geomagnetic field through the motion of fluid in the Earth's outer core. According to Fuller, Herrero-Bervera, and Laj (1996), "This is admittedly a little mysterious and comes about because magnetic field lines are trapped in electrical conductors, such as the fluid of the outer core."
While the trapping of magnetic field lines has important technical applications, scientists remain largely unfamiliar with it in everyday life because the atmosphere in which humans live is a poor electrical conductor.
According to Fuller et al., two cases of special interest to scientists are the Alpha and Omega effects. The Alpha effect describes the lifting and twisting of toroidal field lines by cyclonic convection, which can be driven by thermal or compositional buoyancy. The Omega effect describes the stretching of lines of force into a toroidal shape as they penetrate the core, caused by an increase in angular rotation.
The second process involved in regenerating the Earth's magnetic fields is the diffusion of those fields. Just as with field creation, this second process remains better described than understood. Fuller et al. offer the following analogy: "Just as a drop of colored dye in a swimming pool soon diffuses throughout the pool, so a concentration of magnetic field lines diffuses throughout the outer core."
Despite the relatively mysterious processes involved, scientists have determined that diffusion must take place against the frozen field effect, because it is the balance between these two competing processes that determines the time dependence of the magnetic field — and whether the field decays or is regenerated. Fuller et al. note that on the larger scale of astrophysical or planetary bodies, the magnetic field lines are bound up in fluid motion and distorted, thereafter generating new magnetic fields before they diffuse away. "In the Earth's core, the natural decay time of the magnetic field appears to be about 15,000 years."
These are important considerations because the Earth's geomagnetic field is weak in the sense that it is small compared with the magnetic field required to set, or switch, the magnetization of particles such as those that carry the paleomagnetic record. This helps to ensure that subsequent changes in the field (after the initial magnetization of rock) will not affect that magnetization. However, a paradox remains: "How can the Earth's weak field initially set the magnetization of the particles?" According to Fuller et al., the magnetization of numerous sediments, such as those laid down on the ocean floor, is readily explained through the alignment of detrital magnetic particles in the geomagnetic field. "This preferential alignment in the sediment is locked in as water is lost. The details of the process, however, are less clear. For example, the depth at which the magnetization is locked in, the degree to which the record averages the field values and the lower limits of the field that can be recorded all remain poorly known."
The magnetic effect associated with field-line trapping follows from Michael Faraday's celebrated law of electromagnetic induction, which states that when a magnetic field changes, an electromotive force is established, providing a current that opposes that change. According to Gooding (1996), Faraday remains an important figure in the history of science and technology: "His contributions to modern life are used constantly. All electrical devices involve physical processes related to one of Faraday's many fundamental discoveries (e.g., how to make electricity from magnetism) or to his theoretical vision (e.g., that light propagates as an electromagnetic wave)."
As a result of this magnetic effect, the movement of magnetic field lines with respect to the molten iron of the core is constrained by the current induced in this highly conducting medium. The field line becomes trapped in the fluid, producing what is known as "the frozen field effect." The magnetic field is subsequently carried along with the fluid as it moves in response to the powerful forces being imposed upon it. In this process, the field lines become stretched and twisted, and a new magnetic field is created.
"Describes Lorentz force and electricity-magnetism equivalence"
"Uses Laplace's equation to map field potential and direction"
"Reviews diamagnetism, Arago's disk, and levitation experiments"
From a personal perspective, magnets have always been one of the most fascinating aspects of nature and, notwithstanding the body of knowledge establishing that perpetual motion machines are not possible, appear to represent an inexhaustible source of power for mankind if their secrets can be unlocked. For example, permanent magnets exert a constant force that is used in all electric motors; if this force could be harnessed without the intervention of a mechanical apparatus, there would appear to be free energy available for the taking. While the underlying physics may preclude such an innovation, refinements in how magnetism is applied in the future may help scientists better understand the underlying processes, and a unified theory of the forces of the universe could result.
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