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unit magnetic pole

The strength of a magnetic pole such that two of them, of the same sign, will repel each other with a force of 1 dyne if they are placed 1 centimeter apart in a vacuum. The concept of the unit magnetic pole is used in defining various units in the centimeter-gram-second electromagnetic system of units.

The dimensions of the unit magnetic pole are:

dimensions of unit mag pole L to the three seconds times M to the half, the whole over T

sources

The electrostatic system begins with the definition of the unit of electricity, as determined by the mechanical force between two electrified bodies.

The electro-magnetic system begins with the definition of the strength of a unit magnetic pole, as determined by the mechanical force between two poles.

The form of the definition is precisely the same in both cases. Hence the electrostatic unit of electricity is of the same dimensions as the electro-magnetic unit magnetic pole, and the series of derived units of the one system form a series having respectively the same dimensions as another series belonging to the other system.

J. Clerk Maxwell and Fleeming Jenkin.
On the Elementary Relations between Electrical Measurements.
in
Second Report - Newcastle-on-Tyne, August 26, 1863. Appendix C.
Reports of the Committee on Electrical Standards Appointed by the British Association for the Advancement of Science.
London: E. and F. N. Spon, 1873.
Page 91.

In the electro-magnetic system of measurement, all magnetic and electrical quantities are expressed in units which are derived from a magnetic pole chosen as the pole of unit strength. This unit pole might be defined in many ways; but in order to avoid the fluctuations to which most arbitrary standards would be subject, and to give a convenient system in which work done in the displacements of magnets or conductors, relatively to magnets or to conductors carrying currents, may be estimated without the introduction of arbitrary and inconvenient numerical factors, it is connected by definition with the absolute unit of force. It is defined as a pole which, if placed at unit distance from an equal and similar pole would be repelled with unit force.¹ The poles referred to in this definition are purely ideal, for we cannot separate one pole of a magnet from the opposite pole of the same magnet: but we can by proper arrangements obtain an approximate realisation of the definition. Suppose we have two long, very thin, straight, steel bars, which are uniformly and longitudinally magnetised; their poles may be taken as at their extremities; in fact, the distribution of magnetism in them is such that the magnetic effect of either bar, at all points external to its own substance, would be perfectly represented by a certain quantity of one kind of imaginary magnetic matter placed at one extremity of the bar, and an equal quantity of the opposite kind of matter placed at the other extremity. We may imagine, then, these two bars placed with their lengths in one line, and their blue poles turned towards one another, and at unit distance apart. If their lengths be very great compared with this unit distance, say 100 or 1000 times as great, their red poles will have no effect on the blue poles comparable with the repulsive action of these on one another. But there will be an inductive action between the two blue poles which will tend to diminish their mutual repulsive force, and this we cannot in practice get rid of. The magnitude of this inductive effect is, however, less for hard steel than for soft steel, and we may therefore imagine the steel of the magnets so hard that the action of one on the other does not appreciably affect the distribution of magnetism in either. If, then, two equal blue poles repel one another with unit force, each according to the definition has unit strength.

The magnitude of unit pole is by the above definition made to depend on unit force. Now unit force is defined, according to the system of measurement of forces founded on Newton's Second Law of Motion, the most convenient system, as that force which, acting for unit of time on unit of mass, will give to that mass unit of velocity. The unit pole is thus based on the three fundamental units of length, mass, and time. According to the recommendations of the B. A. Committee, and the resolutions of the Paris Congress, it has been resolved to adopt generally the three units already in very extended use for the expression of dynamical, electrical, and magnetic quantities, namely, the centimetre as unit of length, the gramme as unit of mass, and the second as unit of time; and these units are designated by the letters c.g.s. With these units, therefore, unit force is that force which, acting for one second on a gramme of matter, generates a velocity of one centimetre per second. This unit of force has been called a dyne. The unit magnetic pole, therefore, in the c.g.s. system of units is that pole which, placed at a distance of 1 centimetre from an equal and similar pole, is repelled with a force of 1 dyne. Each of the poles of the long thin magnets of our example above is therefore a pole of strength equal to one c.g.s. unit, if the mutual force between the poles is 1 dyne.

1 The medium between the poles is supposed to be air.

Andrew Gray.
Absolute Measurements in Electricity and Magnetism.
London: Macmillan and Co., 1884.
Pages 20-22.

Subordination of the Magnetic Pole

One of the advantages of the international system [of electric and magnetic units] is that it does not give undue prominence to magnetic pole strength. The complexity of the dimensional expressions of the electromagnetic system and its poor correspondence to the conditions of practice are in part due to its being based upon an unimportant phenomenon. Magnetic poles are of little theoretical or practical importance, while magnetic flux, field intensity, etc. are. The medium is the important thing, as shown by Faraday and Maxwell. Magnetism is becoming more and more regarded as one kind of manifestation of electricity. In the table of the international system given above, magnetic pole strength was defined last, showing that all the other magnetic qualities are definable independently of it. (It can be similiarly subordinated in the equations of the electrostatic system.) A free magnetic pole does not exist in nature, magnetic pole strength does not appear in engineering formulas, and it is consequently a satisfaction to find that it can be dispensed with in the theory also.

J. H. Dellinger.
International System of Electric and Magnetic Units.
Bulletin of the [U.S.] Bureau of Standards, vol 13, no. 4, page 605 (March 6, 1917).