Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/185

If we consider points on the axis on the further side of the point $B$, we find that the resultant force diminishes to the double point $P$, where it vanishes. It then changes sign, and reaches a maximum at $M$, after which it continually diminishes.

This maximum, however, is only a maximum relatively to other points on the axis, for if we draw a surface perpendicular to the axis, $M$ is a point of minimum force relatively to neighbouring points on that surface.

120.] Figure III represents the equipotential surfaces and lines of force due to an electrified point whose charge is 10 placed at $A$, and surrounded by a field of force, which, before the introduction of the electrified point, was uniform in direction and magnitude at every part. In this case, those lines of force which belong to $A$ are contained within a surface of revolution which has an asymptotic cylinder, having its axis parallel to the undisturbed lines of force.

Fig. III

The equipotential surfaces have each of them an asymptotic plane. One of them, indicated by a dotted line, has a conical point and a lobe surrounding the point $A$. Those below this surface have one sheet with a depression near the axis. Those above have a closed portion surrounding $A$ and a separate sheet with a slight depression near the axis.

If we take one of the surfaces below $A$ as the surface of a conductor, and another a long way below $A$ as the surface of another conductor at a different potential, the system of lines and surfaces between the two conductors will indicate the distribution of electric force. If the lower conductor is very far from $A$ its surface will be very nearly plane, so that we have here the solution of the distribution of electricity on two surfaces, both of them nearly plane and parallel to each other, except that the upper one has a protuberance near its middle point, which is more or less prominent according to the particular equipotential line we choose for the surface.

121.] Figure IV represents the equipotential surfaces and lines of force due to three electrified points $A$, $B$ and $C$, the charge of $A$ being 15 units of positive electricity, that of $B$ 12 units of negative electricity, and that of $C$ 20 units of positive electricity. These points are placed in one straight line, so that

$AB=9,\ BC=16,\ AC=25.$

Fig. IV

In this case, the surface for which the potential is unity consists of two spheres whose centres are $A$ and $C$ and their radii 15 and 20.