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discharge will not follow the path that appears to be the best. It may not follow the rod down to the ground, but it may jump across and go down a chimney or may enter the house to some plumbing that comes too near the rod. When installed with reference to these points and to others which are known, a system of rods does afford reasonably good protection. On the other hand, a poorly installed system is of doubtful advantage and may even be dangerous.

389. The law of force between two small electrified spheres. Coulomb was one of the first to make quantitative measurements of the force between two charged bodies. He found that the force between charges on two small spheres varied inversely as the square of the distance between them, and that a measurement of this force enabled him to estimate the size of the charges on the small spheres. In its final form Coulomb's law states that the force between two small charges is directly proportional to the product of the sizes of the charges and inversely proportional to the square of the distance between them. This law may be stated in algebraic form as follows:

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where F is the force, q1 and q2 the charges, d the distance between the charges, and k a constant which depends on the units used and on whether the charges are in air or in some other medium, such as oil.

390. Unit charge. Coulomb's law affords a method of measuring charges; but we must first adopt a unit, or standard, charge. The magnitude of the constant k in equation (7) depends on what units are used for measuring F and q.* We shall choose our unit of charge so that k will be equal to unity when the experiment is performed in air. The equation then becomes

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where the force is measured in dynes and the distance in centimeters.

* See the remarks on a similar constant in section 65.

It is possible, by a method that has been used before, to define the size of a unit charge by taking a special case of equation (8): A unit charge placed 1 centimeter away from an equal charge will repel it with a force of 1 dyne.

This definition and equation (8) are true only when the surrounding medium is air. This will be referred to later.

The unit we have just defined is called the C.G.S. electrostatic (C.G.S.E.S.) unit. Another and much larger unit of quantity of electricity, called the C.G.S. electromagnetic (C.G.S.E.M.) unit, will be defined later. There is still another, called the coulomb, which belongs to the so-called practical system of units. The practical units are merely convenient multiples of the electromagnetic units (see section 522).

30,000,000,000 C.G.S.E.S. units = 1 C.G.S.E.M. unit.
10 coulombs = 1 C.G.S. E. M. unit.

391. A natural unit of electric charge. The fact that an electron always has the same-sized charge on it leads to the suggestion that this is the fundamental charge of nature, the smallest which can exist. This idea has received complete confirmation by the experimental work of R. A. Millikan, who has found that the charge on very small bodies is always, so far as he has tested it, a whole multiple of the electronic charge. The charge on Millikan's small particles never contains any fractional parts of the fundamental charge: the observed charge is always some integral number of electronic charges. Hence it appears that this charge, which may be said to be the natural unit of electricity, can never be subdivided. For this reason it is sometimes called an electrical atom (a word that means something which cannot be divided). This natural unit is a very small charge. AАсcording to Millikan's measurements, which are the most accurate to date, it is equal to 4.774 × 10-10 electrostatic units, or 1.591 × 10-19 coulombs.

The positive charges on the nuclei of atoms are believed to be integral multiples of the natural unit and to vary in magnitude from 1 natural unit on the hydrogen nucleus to 92 on the uranium nucleus.

392. The intensity, or strength, of an electric field. In the region around a charged body there is what is called an electric field. If a small charged body (a charged pith ball, for example) is brought to some point in this field, there will be a force acting on the pith ball. An electric field, then, is a region in which forces will act on charged bodies if they are brought into it.

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Some method must be devised for defining the intensity, or strength, of such a field, for it is frequently necessary to compare two different fields. The usual method is to define the strength, or intensity, of a field by saying that the intensity, or strength, of an electric field is numerically equal to the force that the field would exert on a unit positive charge.

If the force exerted on a unit charge by a certain field is 10 dynes, then the intensity of the field is said to be 10; if the force on a unit charge placed at another point is 12, then the intensity at that place is 12. In this book the symbol I will be used to denote the intensity, or strength, of an electric field.

It follows from the definition of the intensity of a field that a charge q placed in a field at a point where the intensity is F will experience a force given by the equation

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Force on a charge q = Fq.

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393. Electrical lines: the strain theory. It is sometimes convenient, as in the case of magnetic fields, to represent an electric field by lines.

1. A line at any point is always drawn in the direction of the intensity of the field; that is, in the direction of the force which would act on a positive charge if it were brought to that point. 2. The density of the lines at any one place is determined by the intensity of the field at that place.*

In Figs. 239 and 240 the electric field is represented by means of these lines, which always start on a positively charged body and end on a negatively charged one.

If one assumes that these lines have certain properties, the attractions and repulsions of charged conductors can be readily explained. These assumptions are as follows: (1) the lines are under tension and therefore tend to contract; (2) the lines repel each other sidewise.

It has been suggested that the whole phenomenon of charged bodies is, rather, one of the medium: that the medium around the bodies is actually strained in just the way we have imagined these

*The student will notice the similarity between electric lines and magnetic lines. But they must not be confused.

fictitious lines to be. What we have called a charged body is, according to this suggestion, a body with the surrounding medium in a strained condition. This theory is often called the strain theory of the electric field, or sometimes the strained-dielectric

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body is always equal to the inducing charge. Or, stated in terms of electrical lines, the lines from a charged conductor reach out until they meet other conductors, and the total charge at the ends of these lines is equal, and opposite in sign, to the charge on the conductor from which the lines start. For example, when an insulated positive charge is brought into a room, there is brought along with it an induced negative charge on the floor, walls, ceiling, and objects in the room. This induced negative charge is equal to the positive charge on the insulated conductor. We shall now see just how Faraday proved this.

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FIG. 240

Faraday's experiment can be readily understood from Figs. 241 and 242. The uncharged insulated conductor A-an ice pail in the original experiment-is connected to an electroscope E by a wire. When a charged ball B is lowered into A by a silk thread, without touching A, charges are induced on A and on the electroscope, as shown in Fig. 241. If the ball is removed, the leaves of the electroscope collapse, showing that A is left uncharged. When the ball is replaced, the leaves of the electroscope diverge as before. If the ball is now touched to the bottom of the vessel A (Fig. 242), the diverging leaves of the electroscope will show no change whatever. Moreover, when the ball is removed, no charge will be found on it. The explanation is that when the ball touched the bottom of the vessel, the

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that the two-the positive on the ball and the negative on the inside of the vessel-must have been of the same amount. If they had not been equal, the excess charge would have gone to the outside (for "free" charges always go to the outside of a conductor) and would have increased or decreased the charge on the outside. Any change in the outside charge would have been shown by a

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completely surrounds the ball, so that practically all the induced charge is on the inside of A. In the case shown in Fig. 226 (p. 386) the charge induced on B is not equal to that on A. Part of the charges induced by A are on the floor, walls, table, etc. The student should clearly understand that it is the total induced charge which is equal to the inducing charge.

395. The Leyden jar. The Leyden jar forms an interesting example of the application of the principle of electrostatic induction.

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