Page:Elementary Text-book of Physics (Anthony, 1897).djvu/324

310 greater than unity, so that the introduction of such a body into the field involves a loss of energy, and this loss of energy is greater as $$N$$ is greater. Bodies tend to move so as to make their potential energy a minimum, and the given body will therefore move from a place of weaker to a place of stronger electrical force. This conclusion is reached on the supposition that the electrical field is not modified by the presence of the body—a supposition which can be made only when $$K$$ is very nearly equal to unity. When $$K$$ is not nearly equal to unity, the potential is not only diminished by the movement of the body from a place of weaker to a place of stronger electrical force, but also by the movement into it of the tubes of force; for a unit tube of force is associated with less energy in a medium of which the dielectric constant is $$K$$ than in the medium of which the dielectric constant is unity, and the potential energy of the field is therefore diminished by a crowding of the tubes of force into the given body. This process cannot go on indefinitely so that the body includes all the tubes of force of the field, for as some of them enter the body others outside of it are lengthened and their energy is thereby increased. The concentration of the tubes in the body ceases, therefore, when the loss of energy due to their entrance into the body is balanced by the gam of energy due to the lengthening of those outside the body.

A conductor may be looked on as a body having a dielectric constant $$K = \infty.$$ There is no electrical force within a conductor, and the energy lost by the field in consequence of a conductor being introduced into it is $$\frac{F^2 v}{8 \pi},$$ where $$v$$ is the volume of the conductor. This loss of energy is greater as $$F$$ is greater, and the conductor therefore tends to move from a place of weaker to a place of stronger electrical force. There will also be a diminution of potential energy due to the concentration of tubes of force upon the conductor; the conductor disturbs the electrical field and concentrates the tubes of force upon it in a way similar to that of the body just described, but to a greater extent.

269. Cause of the Stress in the Dielectric.—The theory that the