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My goal in writing this paper is two fold. Goal one is to try and understand how a stationary magnet exerts force by means of a magnetic field (even across a complete vacuum). Frequently, electromagnetic fields are compared to the gravitational field. Goal two is to explore the similarities between the two types of fields to see if comparison throws any light on the mechanism of magnetic field generation.
The term action-at-a-distance is often used to describe forces that travel through space and exert their effect without directly touching the objects acted upon. Newton's idea of instantaneous action-at-a-distance has been replaced by the modern action-at-a-distance which is transmitted at the speed of light so as to avoid conflict with Relativity Theory (Hoyle and Narlikar 1974). The term "field theory" either replaces action-at-a-distance or is used as the means by which action-at-a-distance transmits force. In this paper "field" will represent the means of transmitting forces such as electromagnetism and gravity, avoiding the need for the term action-at-a-distance.
Magnetic fields are frequently compared to gravitational fields. Gravitational fields cause a curvature of space-time. That curvature of space-time provides a mechanism for the gravitational attraction between masses. A magnet also causes a curvature of space-time. In fact a magnet can cause space-time curvature in several distinct ways.
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A magnet has mass which will exert gravitational attraction and therefore curve space-time. Furthermore, a magnet produces a magnetic field which has both energy and momentum. Momentum can be demonstrated by the fact that a magnet will produce a force on charged particles, another magnet, or ferromagnetic materials. Both energy and momentum add to a gravitational field in the same way as mass. Therefore the magnetic field itself causes a gravitational field which will produce space-time curvature in addition to the curvature caused by the mass of the magnet.
However, the gravitational field and consequent gravitational attraction exerted by a magnet and its magnetic field aren't strong enough to play much of a role in how magnets attract (let alone repel) other objects. (http://www.sciam.com/askexpert_question.cfm/articleID=000245A8-3-1C71-84A...)
One difference between gravitational and electromagnetic fields is that electromagnetic fields can both attract and repel whereas gravitational fields only act in one direction. Virtual photons can cause both attractive and repulsive forces between charges by the transfer of momentum http://math.ucr.edu/ home/baez/physics/Quantum/virtual_particles.html. However, both mass and energy contribute to gravitational fields. Dark energy is reported to exert an anti-gravity force (Scientific American February 2007). This supposed anti-gravity force might (or might not) parallel the repulsive magnetic force.
The original reason for focusing on the field generated by a stationary magnet was to simplify the issue since a moving magnet generates an electric field. Also it takes work to move a magnet, so it is logical that the work would be a source of energy that enables the magnet to exert force.
Although a stationary magnet cannot affect a stationary charge, it can affect another magnet or ferromagnetic material which is not moving relative to the first magnet. At first glance this seems much simpler since there are no moving charges and no moving magnets. However the electrons in a magnet do move. This movement of the electrons represents moving charges and therefore generates a magnetic field.
Initially, the way a magnet can move other objects seems to violate the law of conservation of energy; work is apparently being accomplished without the expenditure of energy. However, when a magnet, through its magnetic field, displaces a moving charged particle, no work is done because the force is perpendicular to the displacement of the particle (work equals force over the distance the force acts).
A magnet cannot change the kinetic energy of a charged particle; only the particle's direction changes (Serway and Jewett 2004). Therefore, a magnet cannot act upon a charged particle that is at rest relative to the magnet since that would change the particle's kinetic energy.
When two magnets have the proper orientation, one magnet can be used to push the other magnet. However, no work is done (at least by the magnet), because work must be done to push the first magnet and that work is transferred through the magnetic field of both magnets in order to exert a force on the second magnet.
When one magnet pulls another magnet the energy comes from the energy stored in both magnets' magnetic fields. How does that energy end up in the magnetic fields in the first place? If two magnets are together initially, it will take a force to separate them. It seems logical that force could be stored in the fields. If a magnet is constructed separate from any other magnet, the energy must come from the energy expended during construction.
A magnet's ability to generate a magnetic field to transmit force comes from the alignment of its internal moving charges, i.e. electrons (atom nuclei generate insignificant magnetic moment). In most objects, the electron paths are not aligned and therefore no magnetic moment is generated.
The moving electrons in a magnet's atoms generate an electric current (I) in time (T) as follows; I = e/T = with e being the charge of the
electron, v the velocity, and r the radius of the electron's orbit. Magnetic moment () is the product of the current (I) x the area within the electron's orbit (A). A=, so ==. Since angular momentum of the magnet's electron (L) = mvr (m is mass of electron),.
There is another component of the angular momentum resulting from the magnet's spin. The point of all this is that the amount of angular momentum that can be transmitted by a magnet's magnetic field is proportional to the magnetic moment of the magnet's electrons and the spin of the electrons (Serway and Jewett 2004).
Charge generates electromagnetic fields. These electromagnetic fields transmit the charge's energy, momentum, and angular momentum. Even static fields can store momentum and angular momentum (Griffiths 1999).
The initial question of "How does a magnet generate force?" may resolve into a separate question; "How do charged particles exert force?" The force generated by charged particles is described by Coulomb's Law; F= k q1q2/r^2 (force equals the proportionality constant k times charge 1 times charge 2 divided by the square of the distance between the charges).
Coulomb's Law is very similar to the formula for gravitational force; F= G m1m2/r^2 (force equals the gravitational constant times mass 1 times mass 2 divided by the square of the distance between the masses). The mechanism by which charged particles interact through photons (real or virtual) may in some way parallel the way gravity is supposedly mediated by gravitons.
Feynman, Richard P. (1985).QED. The Strange Theory of Light and Matter. Princeton University Press.157 pages.
Griffiths, David J. (1999). Introduction to Electrodynamics. 3rd Edition. Prentice Hall.576 pages.
Hoyle, Fred, and Narlikar, J. V. (1974). Action at a Distance in Physics and Cosmology. W.H. Freeman and Company.266 pages.
Penrose, Roger. (2006). The Road to Reality: A Complete Guide to the Laws of the Universe.Alfred A. Knopf. 1136 pages.
Serway, Raymond A., and Jewett, John J. (2004). Physics for Scientists and Engineers.6th Edition. Brooks/ Cole- Thomson Learning. 1283 pages.
Scientific American (February 2007). Volume 296 Number 2 Pages 35-41.
Website of Fermilab.
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