Page:Elementary Text-book of Physics (Anthony, 1897).djvu/304

290 point within it the same. Electrical force depends on the space rate of change of potential, and not on its absolute value. Hence the changes without the closed conductor will have no effect on bodies within it. Further, any electrical operations whatever within the closed conductor will not change the potential of points outside it. For, whatever operations go on, equal amounts of positive and negative electricity always exist within the conductor, and hence the potential of the conductor remains unaltered. Hence electrical experiments performed within a closed room yield results which are as valid as if the experiments were performed in free space.

The advantage gained by the use of the idea of potential in discussions of electrical phenomena may be illustrated by a statement of the process of charging a conductor by induction described in § 252 (3). To fix our ideas, let us suppose that the field of force is due to a positively electrified sphere, and that the body to be charged is a long cylinder. When this cylinder, previously in contact with the earth and therefore at zero potential, is brought end on to a point near the sphere, it is in a region of positive potential, and is itself at a positive potential. If we consider the original potentials at the points in the region now occupied by the cylinder, it is easily seen that the potential of points nearer the sphere was higher than that of those more remote. When the cylinder is brought into the field, therefore, the portion nearer the sphere is temporarily raised to a higher potential than the portion more remote. The difference of potential between these portions is annulled by a fiow of electricity from the points of higher potential to those of lower potential at a rate depending on the conductivity of the cylinder. The end of the cylinder nearer the sphere is negatively charged, the end more remote is positively charged, and the two charged portions are separated by a line on the surface, called the neutral line, on which there is no charge.

If the cylinder be now joined to ground, a flow of electricity takes place through the ground connection, and it is brought to zero potential. The potential of the cylinder is therefore everywhere lower than the original potentials of the points in the region