Page:Elementary Text-book of Physics (Anthony, 1897).djvu/277

§ 242] a continuous surface distribution over the end of the bar, then $$\frac{m}{s}$$ is also the density of that distribution.

The dimensions of magnetic density follow from this definition. They are $$\left[ \frac{m}{s} \right] = \frac{M^{\tfrac{1}{2}}L^{\tfrac{3}{2}}T^{-1}}{L^2} = M^{\tfrac{1}{2}}L^{-\tfrac{1}{2}}T^{-1}.$$

Coulomb showed, by oscillating a small magnet near different parts of a long bar magnet, that the magnetic force at different points along it gradually increases from the middle of the bar, where it is imperceptible, to the extremities. This would not be the case if the bar magnet were made up of equal straight rows of magnetic molecules in contact, placed side by side. With such an arrangement there would be no force at any point along the bar, but it would all appear at the two ends. The mutual interaction of the molecules of contiguous rows makes such an arrangement, however, impossible.

In the earth's magnetic field, in which the lines of magnetic force may be considered parallel, a couple will be set up on any magnet, so magnetized as to have only two poles, due to the action of equal quantities of north and south magnetism distributed in the magnet. The points at which the forces making up this couple are applied are the poles of the magnet, and the line joining them is the magnetic axis. These definitions are more precise than those which could be given at the outset.

242. Action of One Magnet on the Other.— The investigation of the mechanical action of one magnet on another is important in the construction of apparatus for the measurement of magnetism.

(1) To determine the potential of a short bar magnet at a point distant from it, let $$NS$$ (Fig. 74) represent the magnet of length $$2l,$$ the poles of which are of strength $$m,$$ and let the point $$P$$ be at a distance $$r$$ from the centre of the magnet, taken as origin.