Glass (passed through a Bunsen flame).

Silk.

Wood.

Sealing wax.

Hard rubber.

Sulphur.

LAW OF FORCE AND DISTRIBUTION OF CHARGE.

527. Coulomb's Law.-The French physicist Coulomb (1784) investigated the law of force between two electrified bodies. using a torsion wire balance, illustrated in figure 286. By means of a very fine wire a light horizontal bar of shellac, glass, or other insulating material is suspended

inside of a glass jar by which it is screened from air currents. On the end of the suspended bar is a light pith ball n which is covered with gold foil. A metal ball m mounted on the end of an insulating glass rod can be introduced into the glass jar through a hole in the

cover.

To use the instrument remove the ball m and by means of the graduated head from which the wire is suspended turn the wire until the ball n hangs exactly in the place of m. Now give a charge to m and introduce it into the jar. At first n is attracted and touches m, the charge then divides between the two since both balls are conductors, and immediately n is repelled to such a distance that the twist in the wire balances the force of repulsion. The distance between the balls is observed and also the number of degrees through which the wire is twisted.

FIG. 286.-Coulomb's balance.

Now increase the twist in the wire by means of the graduated head, thus forcing n toward m. It will be found that when the two are at onehalf the first distance the force of repulsion as measured by the twist in the wire is four times as great.

To study the effect of changing the quantity of charge, a second insulated brass ball is taken of the same size as mand mounted on a glass

rod in the same way. the jar and touched to the other similar ball which has no charge. Immediately the charge divides equally between the two (since they are alike) and m now has only half the charge which it had at first. If it is carefully introduced without permitting it to touch n, the charge on the latter will not be changed, and if the force is observed when the balls are the same distance apart as in the first experiment it will be found that the force is only one-half as great.

The ball m with its charge is now withdrawn from

From many such experiments Coulomb concluded that the force between two given charged bodies, provided they are small compared with the distance between them, is inversely proportional to the square of the distance and directly proportional to the amounts of their charges.

This law may be expressed algebraically thus

where F represents the force, K is a constant, and r is the distance between the centers of the two bodies whose charges are represented by q and q'.

The constant K depends on the units that may be used, and also, as was shown by Faraday, on the medium between the two charged bodies.

528. Unit Charge.—Unit charge or unit quantity of electricity, in the electrostatic system of units, is defined as that quantity which when placed one centimeter from an equal charge in vacuum repels it with a force of one dyne.

The force in dynes between two electric charges in vacuum may therefore be expressed by the formula

where the quantities q and q' are measured in electrostatic units and where r is the distance between the charges, measured in centimeters.

When the charges are in any other medium the force is usually less and the formula is

where K is a constant usually greater than one, known as the specific inductive capacity or dielectric constant of the medium.

The force between two charges in air is appreciably the same as in vacuum, for the specific inductive capacity of air is greater than that of vacuum by only about one part in 2000.

529. Distribution. The distribution of an electric charge may be examined by means of a little metal disc mounted on an insulating handle and known as a proof plane. If the disc is placed flat against the surface of the charged and insulated pail shown in figure 287 and then removed, it will carry away a charge which may be tested by the gold-leaf electroscope. When examined in this way it is found that the

Cavity

Conductor

FIG. 287.-Distribution
on pail.

FIG. 288.-Density of distribution indicated
roughly by dotted line.

greatest charge is obtained from the outer surface of the pail near its upper edge and on the outer corner at the bottom, less is found on the middle of the side and none at all in the interior except near the upper edge.

When there is a metal cover on the pail, absolutely no charge can be found on any part of the interior.

Other irregular bodies may be examined in the same way and it will be found that the greatest density of charge is at corners and knobs projecting outward. For example, in a conductor shaped as in figure 288 the greatest density will be found on the projecting point on the left, no charge will be obtained in the cavity even though there is a sharp point there, and very little will be found toward the bottom of the dimple on the right end.

530. Charge Entirely on the Surface of a Conductor.The following experiment was carried out independently by Cavendish and Biot.

A metal ball having two closely fitting hemispherical metal cups which were provided with insulating handles, was insulated

FIG. 289.

and then charged strongly with electricity.

When the cups were

simultaneously removed they were found to have the entire charge, the ball being left without any trace of electrification, showing that the whole charge was on the surface.

531. Discharge from Points.-The density of charge on sharp projecting points of conductors may be so great that the charge will escape to the air. This discharge is accompanied by a stream of air which, if the point is connected with an electrical machine, may be strong enough to blow out a candle or turn a little wheel with light vanes, or if the point from which the discharge takes place is movable it will be driven backward as illustrated in figure 290. Conductors which are designed to hold electrical charges should therefore have all projecting parts or corners carefully rounded, otherwise they will be rapidly discharged.

FIG. 290.-Electric wind.

532 Frictional Electric Machine. The early forms of electrical machines were frictional; the one illustrated in figure 291 is a good type of this class. A circular glass plate is mounted

firmly on an axle so that it can be turned between leather covered rubbers, which are pressed against the glass by a spring. The charge from the glass is received by a metal conductor which is on an insulating support of glass or of hard rubber. From this conductor there are two branches which reach out, one on each side of the glass plate, and on the inside of each is a row of sharp metal points

projecting toward the

glass plate, like the teeth of a comb. The electric charge excited on the glass by the rubbers is carried under the combs by the turning of the plate, and through them it readily passes from the glass into the conductor.

FIG. 291.-Electrical machine.

At the same time that the plate is positively electrified the rubbers become negatively charged and should be connected by a chain or wire with the ground to permit this negative charge to escape. It is usual also to have the lower half of the glass plate covered with a silk bag which prevents the escape of electricity from the glass as it turns.

Problems.

1. Two small conducting balls of the same size and 6 cm. apart have charges +36 and -4, respectively. What is the force between them? Also what will the force become if they are touched together and then placed as before?

2. Two pith balls, each weighing 1 grm. and suspended from the same point by threads 30 cm. long, are equally charged and repelling each other, hang 8 cm. apart. What is the charge on each ball?

INDUCTION.

533. Induction.-When a conductor having no charge is insulated and then brought near a positively charged body, such as A, figure 292, it is found to be negatively electrified on the side next to A and positively electrified on the farther side. This can readily be tested by means of the proof plane and electroscope.