Physics of Magnetism An Overview of the Exciting World of the Modern Physics of Magnetism and Magnetic Fields

The Physics of Magnetism and Magnetic Fields

Today, 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 many people. As can be seen in the graphic on the cover, magnetic field lines are a way to visualize the magnetic field a magnet produces. Magnets produce vector fields at all points in the space around it.

This field can be defined by measuring the force the field exerts on a moving charged particle, such as an electron.

The physics of magnetism require 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: = q. A magnetic field is the result of a cross product between two vectors: For example, two such vectors in the plane of this page of text with an angle between them are illustrated in Figure 1 below.

Figure 1. The Magnetic Field [Source: University of Winnipeg Physics Department].

These calculations become important when considering reversals in the earth's magnetic fields, which were first described by Walter Elsasser and Sir Edward Bullard during the mid-20th century. Today, the general principles of such regeneration of magnetic fields are well established and represent an apparently a common phenomenon in the universe.

There are two fundamental processes involved in the maintenance of the earth's magnetic field.

The first process involves the creation of new magnetic fields from the ambient geomagnetic field through the motion of the fluid in the earth's outer core. According to Fuller and his associates, "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 lines has important technical applications, scientists remain unfamiliar with it in everyday life because the atmosphere in which humans live on earth is a poor electrical conductor.

The magnetic effect described above follows from Michael Faraday's celebrated law of electromagnetic induction, which advises that when a magnetic field changes, an electromotive force is established, thereby providing a current to oppose that field 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 the 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 is trapped in the fluid resulting in 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.

According to Fuller et al., two cases of special interest to scientists are the Alpha and the Omega effects. The Alpha describes the lifting and twisting of the toroidal field lines by cyclonic convection, which could be driven by thermal or compositional buoyancy; the Omega describes the stretching of lines of force into a toroidal shape as they penetrate the core, which would be caused by an increase in angular rotation.

The second process involved in regenerating of earth's magnetic fields is the diffusion of the fields. Just as with the creation of new magnetic fields, this second process remains better described than understood. Fuller et al. provide the following analogy to help illustrate the underlying processes involved: "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 here, 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 away or is regenerated. Fuller et al. point out that on the larger scale of astro-physical or planetary bodies, the magnetic field lines are bound up in...

"In the earth's core, the natural decay time of the magnetic field appears to be about 15,000 years."
These are important considerations for scientists today 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 the rock) will not affect that magnetization; however, there still remains yet another paradox: "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 the 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."

What is known, though, is that the only force a charged particle at rest feels, other than gravity, is an electric force. According to Krauss (1993), "You can put the strongest magnet in the world next to such a particle and it will just sit there, oblivious. On the other hand, if you move a charged particle in the presence of a magnet, the particle will experience a force that changes its motion."

This phenomenon is known as the Lorentz force, named after the Dutch physicist Henrik Lorentz, who succeeded in closely formulating special relativity before Einstein. The Lorentz force assumes a highly interesting form. If a charged particle moves horizontally between the poles of a magnet, as shown in Figure 2 below, the force on the particle will be upward, perpendicular to its original motion:

Figure 2. Illustration of Lorentz force [Source: Krauss, 107].

These two general features are sufficient to demonstrate that an electric force to one person is a magnetic force to another. "Electricity and magnetism are thus as closely related as the circle and rectangle on the cave wall" (emphasis added).

This close relationship between electricity and magnetism can be readily seen by considering the particle in Figures 2 above. If this was being observed it a laboratory setting, a researcher could watch it move and get deflected; consequently, it could be determined that the force acting on it was the magnetic Lorentz force. If the researcher was in a laboratory traveling at a constant velocity alongside the particle, though, the particle would not appear to be moving relative to the researcher, but the magnet would be. This phenomenon is illustrated in Figure 3 below.

Figure 3. Relationship between Electricity and Magnetism [Source: Krauss, 108].

Because a charged particle at rest can feel only an electric force, the force acting on the particle in Figure 3 must be electric.

Ever since Galileo, in fact, scientists have known that the laws of physics must appear the same for any two observers moving at a constant relative velocity. As a result, there is no way to conclusively prove that it is the particle that is moving and the magnets that are standing still, or vice versa. "Rather, we can merely conclude that the particle and the magnets are moving relative to each other."

Having establishing that electricity and magnetism share these commonalities, the next step involves identifying some way of measuring the field at any given point. Von Nostran's Scientific Encyclopedia provides the example of a region of space in which there is an electric field (due to electric charges in the vicinity), but with no free electricity; in other words, no such space charge as exists in a vacuum tube in operation. "At any point in this space there is an electric potential, which varies with the position of the point and is therefore a function of its coordinates."

It is shown in electrostatic theory that if the potential satisfies Laplace's equation, it is possible to trace the lines of force and equipotential surfaces in the region, by means of special solutions of Laplace's equation, known as "harmonic functions"; the latter functions satisfy the "boundary conditions" imposed by the arrangement of the neighboring charges. The form of the equation is to be used depends upon the system of coordinates which is most conveniently adapted to the shape and arrangement of the charged bodies (Denker suggests…