The Theory Of Magnetism Made Simple

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Electromagnetism has continued to develop into the 21st century, being incorporated into the more fundamental theories of gauge theory, quantum electrodynamics, electroweak theory, and finally the standard model.

As a consequence of Einstein's theory of special relativity, electricity and magnetism are fundamentally interlinked. Both magnetism lacking electricity, and electricity without magnetism, are inconsistent with special relativity, due to such effects as length contraction, time dilation, and the fact that the magnetic force is velocity-dependent. However, when both electricity and magnetism are taken into account, the resulting theory (electromagnetism) is fully consistent with special relativity.[11][17] In particular, a phenomenon that appears purely electric or purely magnetic to one observer may be a mix of both to another, or more generally the relative contributions of electricity and magnetism are dependent on the frame of reference. Thus, special relativity \"mixes\" electricity and magnetism into a single, inseparable phenomenon called electromagnetism, analogous to how general relativity \"mixes\" space and time into spacetime.

Some organisms can detect magnetic fields, a phenomenon known as magnetoception. Some materials in living things are ferromagnetic, though it is unclear if the magnetic properties serve a special function or are merely a byproduct of containing iron. For instance, chitons, a type of marine mollusk, produce magnetite to harden their teeth, and even humans produce magnetite in bodily tissue.[23] Magnetobiology studies the effects of magnetic fields on living organisms; fields naturally produced by an organism are known as biomagnetism. Many biological organisms are mostly made of water, and because water is diamagnetic, extremely strong magnetic fields can repel these living things.

While heuristic explanations based on classical physics can be formulated, diamagnetism, paramagnetism and ferromagnetism can be fully explained only using quantum theory.[24][25]A successful model was developed already in 1927, by Walter Heitler and Fritz London, who derived, quantum-mechanically, how hydrogen molecules are formed from hydrogen atoms, i.e. from the atomic hydrogen orbitals u A {\\displaystyle u_{A}} and u B {\\displaystyle u_{B}} centered at the nuclei A and B, see below. That this leads to magnetism is not at all obvious, but will be explained in the following.

The simplest model displaying ferromagnetism is named after Nagaoka. Its description follows\\[N\\] electrons in a nondegenerate band (\\(H_0\\) of Eq. (13) is a good example) are subject to a large, repulsive on-site potential such that no two electrons, even though they have opposite spins, can occupy the same site. The hopping matrix element that connect 2 neighboring sites is \\(t\\ .\\) Thus the Hamiltonian, known as the Hubbard Hamiltonian if \\(U^*\\) is finite, is:

Physics and mathematics have always had a close relation, but none closer than the calculation of magnetism using concepts in analysis, number theory, algebra and group theory. We have tried to show this in the present article by concentrating on just a few of the topics that have come up in an evolving theory of magnetism. Hopefully, an even broader understanding of magnetic phenomena will follow new mathematics and mathematical concepts.

Amber is a yellowish, translucent mineral. As early as 600 BC the Greek philosopher, Aristophanes was aware of its peculiar property: when rubbed with a piece of fur, amber develops the ability to attract small pieces of material such as feathers. For centuries this strange, inexplicable property was thought to be unique to amber. This strange effect remained a mystery for over 2000 years, until, around AD 1600, Dr William Gilbert investigated the reactions of amber and magnets and first recorded the word 'Electric' in a report on the theory of magnetism.

It was known as early as 1600 that the attractive or repulsive force diminishes as the charges are separated. This relationship was first placed on a numerically accurate, or quantitative, foundation by Joseph Priestley, a friend of Benjamin Franklin. In 1767, Priestley indirectly deduced that when the distance between two small, charged bodies is increased by some factor, the forces between the bodies is reduced by the square of the factor. For example, if the distance between charges is tripled, the force decreases to one-ninth its former value. Although rigorous, Priestley's proof was so simple that he did not strongly advocate it. The matter was not considered settled until 18 years later, when John Robinson of Scotland made more direct measurements of the electrical force involved.

Andre Marie Ampere, a French mathematician who devoted himself to the study of electricity and magnetism, was the first to explain the electro-dynamic theory. He showed that two parallel wires, carrying current, attracted each other if the currents flowed in the same direction and opposed each other if the currents flowed in opposite directions. He formulated in mathematical terms, the laws that govern the interaction of currents with magnetic fields in a circuit and as a result of this the unit of electric current, the amp, was derived from his name. An electric charge in motion is called electric current. The strength of a current is the amount of charge passing a given point per second, or I = Q/t, where Q coulombs of charge passing in t seconds. The unit for measuring current is the ampere or amp, where 1 amp = 1 coulomb/sec. Because it is the source of magnetism as well, current is the link between electricity and magnetism.

In 1830, Joseph Henry (1797-1878), discovered that a change in magnetism can make currents flow, but he failed to publish this. In 1832 he described self-inductance - the basic property of inductor. In recognition of his work, inductance is measured in henries. The stage was then set for the encompassing electromagnetic theory of James Clerk Maxwell. The variation of actual currents is enormous. A modern electrometer can detect currents as low as 1/100,000,000,000,000,000 amp, which is a mere 63 electrons per second. The current in a nerve impulse is approximately 1/100,000 amp; a 100-watt light bulb carries 1 amp; a lightning bolt peaks at about 20,000 amps; and a 1,200-megawatt nuclear power plant can deliver 10,000,000 amps at 115 V.

Faraday was greatly interested in the invention of the electromagnet, but his brilliant mind took earlier experiments still further. If electricity could produce magnetism, why couldn't magnetism produce electricity. In 1831, Faraday found the solution. Electricity could be produced through magnetism by motion. He discovered that when a magnet was moved inside a coil of copper wire, a tiny electric current flows through the wire. H.C. Oersted, in 1820, demonstrated that electric currents produce a magnetic field. Faraday noted this and in 1821, he experimented on the theory that, if electric currents in a wire can produce magnetic fields, then magnetic fields should produce electricity. By 1831, he was able to prove this and through his experiment, was able to explain, that these magnetic fields were lines of force. These lines of force would cause a current to flow in a coil of wire, when the coil is rotated between the poles of a magnet. This action then shows that the coils of wire being cut by lines of magnetic force, in some strange way, produces electricity. These experiments, convincingly demonstrated the discovery of electromagnetic induction in the production of electric current, by a change in magnetic intensity.

The Englishman William Gilbert (1540-1603) was the first to investigate the phenomenon of magnetism systematically using scientific methods. He also discovered that the Earth is itself a weak magnet. Early theoretical investigations into the nature of the Earth's magnetism were carried out by the German Carl Friedrich Gauss (1777-1855). Quantitative studies of magnetic phenomena initiated in the eighteenth century by Frenchman Charles Coulomb (1736-1806), who established the inverse square law of force, which states that the attractive force between two magnetized objects is directly proportional to the product of their individual fields and inversely proportional to the square of the distance between them. Danish physicist Hans Christian Oersted(1777-1851) first suggested a link between electricity and magnetism. Experiments involving the effects of magnetic and electric fields on one another were then conducted by Frenchman Andre Marie Ampere (1775-1836) and Englishman Michael Faraday (1791-1869), but it was the Scotsman, James Clerk Maxwell (1831-1879), who provided the theoretical foundation to the physics of electromagnetism in the nineteenth century by showing that electricity and magnetism represent different aspects of the same fundamental force field. Then, in the late 1960s American Steven Weinberg (1933- ) and Pakistani Abdus Salam (1926- ), performed yet another act of theoretical synthesis of the fundamental forces by showing that electromagnetism is one part of the electroweak force. The modern understanding of magnetic phenomena in condensed matter originates from the work of two Frenchmen: Pierre Curie (1859-1906), the husband and scientific collaborator of Madame Marie Curie (1867-1934), and Pierre Weiss (1865-1940). Curie examined the effect of temperature on magnetic materials and observed that magnetism disappeared suddenly above a certain critical temperature in materials like iron. Weiss proposed a theory of magnetism based on an internal molecular field proportional to the average magnetization that spontaneously align the electronic micromagnets in magnetic matter. The present day understanding of magnetism based on the theory of the motion and interactions of electrons in atoms (called quantum electrodynamics) stems from the work and theoretical models of two Germans, Ernest Ising (1900- ) and Werner Heisenberg (1901-1976). Werner Heisenberg was also one of the founding fathers of modern quantum mechanics. 153554b96e

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