as a volume expansion under the action of some effective excess pressure Δ P which is uniformly distributed over the surface of the body and replaces the exact distribution given by (5.1). In the first approximation, therefore, the change in volume can be regarded as the result of deformation without change in shape, i.e. To do so, we must bear in mind that, if the deformation is slight (as in fact is true for electrostriction), the effect of the change of shape on the change of volume is of the second order of smallness. If, however, we are interested only in the change in volume, the problem can be solved very simply. A complete determination of the deformation requires a solution of the equations of the theory of elasticity, with the given distribution of forces (5.1) on the surface of the body. Because the force is an extending one, the volume of the body increases. The forces (5.1) on the surface of the conductor result in changes in its shape and volume. If the total force and torque on a conductor are zero, the conductor remains at rest in the field, and effects involving the deformation of the body (called electrostriction) become important. In accordance with the usual expression given by the theory of fields in a vacuum. Thus, for a system of conductors whose potentials are kept constant, the part of the mechanical energy is played not by U, but by In this sense we can say that U pertains to a system which is not energetically closed. Only the energy of the conductors, and not that of the reservoirs, appears in U. ![]() When the whole system of conductors receives charges e a, the energy of the reservoirs connected to them changes by a total of − Σ e aϕ a. On receiving a charge e a, the conductor takes it from the reservoir, whose potential ϕ α is unchanged on account of its large capacitance, although its energy is reduced by e aϕ a. For example, the potential of a conductor can be kept constant by connecting it to another conductor of very large capacitance, a “charge reservoir”. The reason is that, to maintain constant the potential of a moving conductor, it is necessary to use other bodies. If, however, the energy is expressed as a function of the potentials of the conductors, and not of their charges, the calculation of the forces from the energy requires special consideration.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |