induction, in electricity and magnetism

induction, in electricity and magnetism, common name for three distinct phenomena.

Electromagnetic induction is the production of an electromotive force electromotive force, abbr. emf, difference in electric potential, or voltage, between the terminals of a source of electricity, e.g., a battery from which no current is being drawn. When current is drawn, the potential difference drops below the emf value.
..... Click the link for more information. (emf) in a conductor as a result of a changing magnetic field field, in physics, region throughout which a force may be exerted; examples are the gravitational, electric, and magnetic fields that surround, respectively, masses, electric charges, and magnets. The field concept was developed by M.
..... Click the link for more information. about the conductor and is the most important of the three phenomena. It was discovered in 1831 by Michael Faraday and independently by Joseph Henry. Variation in the field around a conductor may be produced by relative motion between the conductor and the source of the magnetic field, as in an electric generator generator, in electricity, machine used to change mechanical energy into electrical energy. It operates on the principle of electromagnetic induction , discovered (1831) by Michael Faraday.
..... Click the link for more information. , or by varying the strength of the entire field, so that the field around the conductor is also changing. Since a magnetic field is produced around a current-carrying conductor, such a field can be changed by changing the current. Thus, if the conductor in which an emf is to be induced is part of an electric circuit, the induction can be caused by changing the current in that circuit; this is called self-induction. The induced emf is always such that it opposes the change that gives rise to it, according to Lenz's law Lenz's law, physical law, discovered by the German scientist H. F. E. Lenz in 1834, that states that the electromotive force (emf) induced in a conductor moving perpendicular to a magnetic field tends to oppose that motion.
..... Click the link for more information. . Changing the current in a given circuit can also induce an emf in another, nearby circuit unconnected with the original circuit; this type of electromagnetic induction, called mutual induction, is the basis of the transformer transformer, electrical device used to transfer an alternating current or voltage from one electric circuit to another by means of electromagnetic induction .
..... Click the link for more information. .

Electrostatic induction is the production of an unbalanced electric charge on an uncharged metallic body as a result of a charged body being brought near it without touching it. If the charged body is positively charged, electrons in the uncharged body will be attracted toward it; if the opposite end of the body is then grounded, electrons will flow onto it to replace those drawn to the other end, the body thus acquiring a negative charge after the ground connection is broken. A similar procedure can be used to produce a positive charge on the uncharged body when a negatively charged body is brought near it. See electricity electricity, class of phenomena arising from the existence of charge . The basic unit of charge is that on the proton or electron —the proton's charge is designated as positive while the electron's is negative.
..... Click the link for more information. .

Magnetic induction is the production of a magnetic field in a piece of unmagnetized iron or other ferromagnetic substance when a magnet is brought near it. The magnet causes the individual particles of the iron, which act like tiny magnets, to line up so that the sample as a whole becomes magnetized. Most of this induced magnetism is lost when the magnet causing it is taken away. See magnetism magnetism, force of attraction or repulsion between various substances, especially those made of iron and certain other metals; ultimately it is due to the motion of electric charges.
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induction, in logic

induction, in logic logic, the systematic study of valid inference. A distinction is drawn between logical validity and truth. Validity merely refers to formal properties of the process of inference.
..... Click the link for more information. , a form of argument in which the premises give grounds for the conclusion but do not necessitate it. Induction is contrasted with deduction deduction, in logic , form of inference such that the conclusion must be true if the premises are true. For example, if we know that all men have two legs and that John is a man, it is then logical to deduce that John has two legs.
..... Click the link for more information. , in which true premises do necessitate the conclusion. An important form of induction is the process of reasoning from the particular to the general. Francis Bacon in his Novum Organum (1620) elucidated the first formal theory of inductive logic, which he proposed as a logic of scientific discovery, as opposed to deductive logic, the logic of argumentation. Both processes, however, are used constantly in research. By observation of events (induction) and from principles already known (deduction), new hypotheses are formulated; the hypotheses are tested by applications; as the results of the tests satisfy the conditions of the hypotheses, laws are arrived at—by induction; from these laws future results may be determined by deduction. David Hume Hume, David (hy

m), 1711–76, Scottish philosopher and historian.
..... Click the link for more information. has influenced 20th-century philosophers of science who have focused on the question of how to assess the strength of different kinds of inductive argument (see Nelson Goodman Goodman, Nelson, 1906–, American philosopher, b. Somerville, Mass., grad. Harvard (Ph.D. 1941). He taught at Tufts (1945–46), the Univ. of Pennsylvania (1946–64), and Brandeis Univ.
..... Click the link for more information. ; Sir Karl Raimund Popper Popper, Sir Karl Raimund, 1902–94, Anglo-Austrian philosopher, b. Vienna. He became familiar with the Vienna circle of logical positivists (see logical positivism ) while a student at the Univ. of Vienna (Ph.D., 1928). He taught at Canterbury Univ.
..... Click the link for more information. ). For a classic account of inductive arguments see J. S. Mill, System of Logic (1843).

Bibliography

See also R. Swinburne, ed., The Justification of Induction (1974); J. Cohen, An Introduction to the Philosophy of Induction and Probability (1989).

induction

In logic, a type of nonvalid inference or argument in which the premises provide some reason for believing that the conclusion is true. Typical forms of inductive argument include reasoning from a part to a whole, from the particular to the general, and from a sample to an entire population. Induction is traditionally contrasted with deduction. Many of the problems of inductive logic, including what is known as the problem of induction, have been treated in studies of the methodology of the natural sciences. See also John Stuart Mill; philosophy of science; scientific method.

The process of generating an electric current in a circuit from the magnetic influence of an adjacent circuit as in a transformer or capacitor.

Electrical induction is also the principle behind the write head on magnetic disks and earlier read heads. To create (write) the bit, current is sent through a coil that creates a magnetic field which is discharged at the gap of the head onto the disk surface as it spins by. To read the bit, the magnetic field of the bit "induces" an electrical charge in the head as it passes by the gap. See inductor.

(logic)

induction - A method of proving statements about well-ordered sets. If S is a well-ordered set with ordering "<", and we want to show that a property P holds for every element of S, it is sufficient to show that, for all s in S,

IF for all t in S, t < s => P(t) THEN P(s)

I.e. if P holds for anything less than s then it holds for s. In this case we say P is proved by induction.

The most common instance of proof by induction is induction over the natural numbers where we prove that some property holds for n=0 and that if it holds for n, it holds for n+1.

(In fact it is sufficient for "<" to be a well-founded partial order on S, not necessarily a well-ordering of S.)