Page:Elementary Text-book of Physics (Anthony, 1897).djvu/275

§ 240] of the truth of the law, and showed by experiment that the action calculated was actually exerted.

All theories of magnetism assume that the force between two magnet poles is proportional to the product of the strengths of the poles. The law of magnetic force is then the same as that upon which the discussion of potential and of flux of force was based. The theorems there discussed are in general applicable in the study of magnetism, although modifications in the details of their application occur, arising from the fact that the field of force about a magnet is due to the combined action of. two dissimilar and equal poles.

If $$m$$ and $$m'$$ represent the strengths of two magnet poles, $$r$$ the distance between them, and $$k$$ a factor depending on the units in which the strength of the pole is measured, the formula expressing the force between the poles is $$k\frac{mm'}{r^2}\cdot$$

240. Definitions of Magnetic Quantities.—The law of magnetic force enables us to define a unit magnet pole, based upon the fundamental mechanical units.

If two perfectly similar magnets, infinitely thin, uniformly and longitudinally magnetized, be so placed that their positive poles are unit distance apart, and if these poles repel one another with unit force, the magnet poles are said to be of unit strength. Hence, in the expression for the force between two poles, $$k$$ becomes unity, and the dimensions of $$\frac{m^2}{r^2}$$ are those of a force. That is, $$\left[ \frac{m^2}{r^2} \right],$$ from which the dimensions of a magnet pole are $$[m] = M^{\tfrac{1}{2}}L^{\tfrac{3}{2}}T^{-1}.$$ This definition of a unit magnet pole is the foundation of the magnetic system of units. The strength of a magnet pole is then equal to the force which it will exert on a unit pole at unit distance.

The product of the strength of the positive pole of a uniformly and longitudinally magnetized magnet into the distance between its poles is called its magnetic moment.