Page:Elementary Text-book of Physics (Anthony, 1897).djvu/323

§ 268] directed toward it. When two such spheres, one charged positively and the other negatively, are brought near each other, the tubes of force in the region between them to some extent coincide, so that the number of tubes of force which pass through unit area in the region between them is greater than that passing through the same area when only one of the spheres is present. On the other hand, the tubes in the region outside both the spheres counteract each other, and the number of tubes of force which pass through unit area in this region is less than when only one of the spheres is present. It may be seen thus roughly, and a diagram of the actual tubes of force in the field shows clearly, that the number of tubes of force which proceed from unit area of either one of the spheres on the surfaces confronting each other is greater than the number which proceeds from unit area on the outer surfaces. The tensions tending to draw the spheres together are thus greater than the tensions tending to separate them, and the spheres therefore appear to attract each other. If the two spheres which are brought near each other have similar charges, the tubes of force in the region between them are opposed to each other and the number of tubes of force in that region is therefore diminished, while in the region outside the two spheres their tubes of force partly coincide and the number is increased. The tension is therefore greater on the outer surfaces of the spheres, and they are pulled apart or appear to repel each other. In these explanations no account has been taken of the inductive action of one sphere on the other.

We may use the results obtained in the last section in the discussion of the forces which act upon a body originally uncharged, having a dielectric constant $$K$$ and brought into an electrical field set up in a medium of which the dielectric constant is different from $$K;$$ for convenience, we will assume it to be unity. Let us assume that the body to be brought into the field is small and represent its volume by $$v.$$ Now, before the body is brought into the field the energy in the volume afterwards occupied by it is $$2\pi N^2 v.$$ The energy in the same volume, after it is occupied by the body, is $$\frac{2 \pi N^2 v}{K}\cdot$$ Now we know by experiment that $$K$$ is always