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86

Galvanism, From Galvani to Ohm.

circle that the motions in opposite parts should have an opposite direction."

Oersted's discovery was described at the meeting of the French Academy on September 11th, 1820, by an academician (Arago) who had just returned from abroad. Several investigators in France repeated and extended his experiments; and the first precise analysis of the effect was published by two of these, Jean-Baptiste Biot (b. 1774, d. 1862) and Félix Savart (b.1791, d. 1841), who, at a meeting of the Academy of Sciences. on October 30th, 1820, announced^[1] that the action experienced by a pole of austral or boreal magnetism, when placed at any distance from a straight wire carrying a voltaic current, may be thus expressed: "Draw from the pole a perpendicular to the wire; the force on the pole is at right angles to this line and to the wire, and its intensity is proportional to the reciprocal of the distance." This result was soon further analysed, the attractive force being divided into constituents, each of which was supposed to be due to some particular element of the current; in its new form the law may be stated thus: the magnetic force due to an element ds of a circuit, in which a current i is flowing, at a point whose vector distance from ds is r, is (in suitable units)

${\frac {i}{r^{3}}}[\mathbf {ds,r} ]$ ^[2] or $\mathrm {curl} {\frac {i\mathbf {ds} }{r}}$ .^[3]

It was now recognized that a magnetic field may be produced as readily by an electric current as by a magnet; and, as Arayo soon showed,^[4] this, like any other magnetic field, is capable of

↑ Annales de Chimie, xv (1820), p. 222; Journal de Phys., xli, p. 51.
↑ If a and b denote two vectors, the vector whose components are ( $a_{y}b_{z}-a_{z}b_{y},a_{z}b_{x}-a_{x}b_{z},a_{x}b_{y}-a_{y}b_{x}$ ) is called the vector product of a and b, and is denoted by [a, b]. Its direction is at right angles to those of a and b, and its magnitude is represented by twice the area of the triangle formed by them.
↑ If a denotes any vector, the vector whose components are ${\frac {\partial \alpha _{z}}{\partial y}}-{\frac {\partial \alpha _{y}}{\partial z}},{\frac {\partial \alpha _{x}}{\partial z}}-{\frac {\partial \alpha _{z}}{\partial x}},{\frac {\partial \alpha _{y}}{\partial x}}-{\frac {\partial \alpha _{x}}{\partial y}}$ is denoted by curl a.
↑ Annales de Chimie, x1 (1820), p. 93.

[1] Annales de Chimie, xv (1820), p. 222; Journal de Phys., xli, p. 51.

[2] If a and b denote two vectors, the vector whose components are ( $a_{y}b_{z}-a_{z}b_{y},a_{z}b_{x}-a_{x}b_{z},a_{x}b_{y}-a_{y}b_{x}$ ) is called the vector product of a and b, and is denoted by [a, b]. Its direction is at right angles to those of a and b, and its magnitude is represented by twice the area of the triangle formed by them.

[3] If a denotes any vector, the vector whose components are ${\frac {\partial \alpha _{z}}{\partial y}}-{\frac {\partial \alpha _{y}}{\partial z}},{\frac {\partial \alpha _{x}}{\partial z}}-{\frac {\partial \alpha _{z}}{\partial x}},{\frac {\partial \alpha _{y}}{\partial x}}-{\frac {\partial \alpha _{x}}{\partial y}}$ is denoted by curl a.

[4] Annales de Chimie, x1 (1820), p. 93.

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