Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/35

 Rh phenomena can be accounted for by supposing that like ends of the magnets repel each other, that unlike ends attract each other, and that the intermediate parts of the magnets have no sensible mutual action.

The ends of a long thin magnet are commonly called its Poles. In the case of an indefinitely thin magnet, uniformly magnetized throughout its length, the extremities act as centres of force, and the rest of the magnet appears devoid of magnetic action. In all actual magnets the magnetization deviates from uniformity, so that no single points can be taken as the poles. Coulomb, however, by using long thin rods magnetized with care, succeeded in establishing the law of force between two magnetic poles.

The repulsion between two magnetic poles is in the straight line joining them, and is numerically equal to the product of the strengths of the poles divided by the square of the distance between them.

374.] This law, of course, assumes that the strength of each pole is measured in terms of a certain unit, the magnitude of which may be deduced from the terms of the law.

The unit-pole is a pole which points north, and is such that, when placed at unit distance from another unit-pole, it repels it with unit of force, the unit of force being defined as in Art. 6. A pole which points south is reckoned negative.

If $$m_1$$ and $$m_2$$ are the strengths of two magnetic poles, $$l$$ the distance between them, and $$f$$ the force of repulsion, all expressed numerically, then

$$ f = \frac{m_1 m_2}{l^2} $$.

But if $$[m]$$, $$[L]$$ and $$[F]$$ be the concrete units of magnetic pole, length and force, then

$$ f[F] = \left[ \frac{m}{L} \right]^2 \frac{m_1 m_2}{l^2} $$

whence it follows that

$$ [m^2] = [L^2 F] = \left[L^2 \frac{ML}{T^2} \right] $$,

or $$ [m] = [L^{\frac{3}{2}} T^{-1} M^{\frac{1}{2}}] $$.

The dimensions of the unit pole are therefore 3/2 as regards length, (-1) as regards time, and 1/2 as regards mass. These dimensions are the same as those of the electrostatic unit of electricity, which is specified in exactly the same way in Arts. 41, 42.