Chapter V 22.docx

CHAPTER V THEORY AS TO THE EXCHANGES OF ENERGY IN ARMATURES 22. Quantitative Meaning of Magnetic Lines of Force. We have hitherto used lines of magnetic force as showing merely the direction of the resultant magnetic force at any point of the field of force, but have not settled how far apart we should draw the lines. We will now extend the definition of 'lines of force' to that they will show the intensity as well as the direction A the magnetic force at the point. The 'intensity of the field' at any point is measured by the mechanical force in dynes acting on a unit north pole at that point, tending to move it in the direction of the line of force. For simplicity, consider first a uniform field, in which all the lines of force are parallel to one another. Draw as nany magnetic lines passing through each square centimetre as there would he dyes acting on t toit pole. The square centimetre is of course to be taken at right angles to the force. Therefore if the field is strong, the lines will be crowded together, if weak, they will be far apart; and the `density ' of the lines will be a measure of the strength of the field. Next as a less simple case consider the field round an isolated magnet pole of strength m. It will consist of lines of force radiating from the pole in all directions. By the second law of magnetic force, the intensity of the field at a distance r cm. front the magnet pole is If then see wish to represent; the force intensity at points on this sphere by the density of shnetahomf force in the same way before, we must draw thee • o ;.-7 lin. pass through each square cm. of the surface of this sphere. Since the area of the surface of a sphere of r cm. radius is 47, sq. cm., there will be 4rr, x - or 4rm lines to be drawn in all. If we produce these same lines to another concentric sphere of radius r, cm., their density will change so that there are .17ret lines to fee, sq. cm., i.e. 7,, to 1 sq. cm., and 7,, is the field intensity at that distance. Thus we see that if we draw the correct number of lines per sq. cm. at one point they will ,ontract or spread out so as to represent correctly the field intensity at all other points of their course. This can he shown to be true of all fields of force, however complicated. Note that if we take In = 1 in the above, we find that there proceed front a unit pole 4e lives of force.' Thus a field of magnetic force can he completely represented by lines of for, the direction of the force at any point being that of the lines of force there and its intensity being the number of such lines to the sq. cm. It is to he understood that field of force which niters from point to point, the force at any point milk not be taken as the number of lines through an actual sq. cm. round the point, but a very much smaller area containing the point must be taken and the number of lines passing through it must be found. Then the • number per sq. cm. at that point ' means the number that would pa. through a aq. cm. if the density were the same all over it it is over the small area. This is exactly analogous to the case of hydrostatic present e at a point.