K1 Electricity

Static Electricity

Electrification by friction between two bodies

The longest known phenomenon, called electric, is observed when you rub two substances against each other. We will start from here, however, note: The decisive aspect is not the friction, but mutual touching of substances, an increase and enlargement of the touching surfaces. The mechanism of the formation of frictional electricity is unknown.

If you rub a (dry) piece of glass strongly with (dry!) silk, the silk sticks to the glass after you release it. If you separate the silk from the glass, but leave it near it, it will again attach itself to the glass like a piece of iron hangs on to a magnet, that is, after they have been rubbed against each other the glass attracts the silk. This attraction is mutual in that also the silk attracts the glass (Action and reaction). What applies to glass and silk is also true for many other substances, when they are rubbed together, even for fluids and gases; however, especially in the case of metals, you must take certain precautionary measures, in order to obtain this phenomenon. These phenomena are called electric after the substance amber (Greek: hlektron = electron) with which they were first observed; their cause is the electricity with which the body is charged, or electrified, and its environment is called an electric field.

To start with, we will extend our knowledge by an experiment. Let G1 and G2 (denoted by ) be two small glass disks, S1 and S2 (denoted by ) two disks made out of silk. Rub 1 and 1 with each other (as many points of the two faces as possible touching each other), then separate them, fix 1 to one end of a plastic needle, 1 to the end of another plastic needle and suspend the needle like a compass needle (Fig. 424). We repeat this with 2 and 2. If we now approach with 1 the disk 1, it moves (by turning the needle) towards 1 - in agreement with what the first experiment told; the same happens with 2 and 2.

But this experiment tells you more: We can interchange the glass disks (replace 2 by 1) or the silk disks (replacing 1 by 2) without changing anything else and observe: 1 and 2 also attract each other and so do 1 and 2. However, if we interchange a glass disk with a silk disk, that is, interchange 1 and 2 or 2 and 1 , they repel each other. The fact that you can replace 1 by 2 tells that their electrical state is the same, the fact that 2 cannot replace 1, that is, attraction is replaced by repulsion, that their electrical states are not the same. We say that the state of 2 is opposite to that of 2, because attraction and repulsion (by which alone the difference in the electric states manifests itself) are for us contrasts; similarly, we call the states of 1and 2 equal, those of 1 and 2 opposite. Our final conclusion is that oppositely electrified bodies attract, equally electrified bodies repel each other.

Apart from glass and silk, many other substances exhibit this confrontation after they have been rubbed together: Always one partner corresponds to the rubbed glass, the other to the rubbed silk. A small glass sphere, rubbed with silk and suspended by a thread, will attract (repel) its partner silk (glass). With the aid of such a pendulum (Fig. 425), you can arrange substances in a sequence, in which on being rubbed successive partners take the place of glass (or silk). This friction-electric sequence is approximately: Glass, fur, paper, cotton, silk, metals, hard rubber, resins, sulphur. However, this sequence is quite uncertain. The position of a substance in the sequence depends on circumstances not under your control like the kind of the surface of the body, the mode of rubbing, etc.

Experience has shown that for glass the most effective rubbing agent is silk, for resins flannel. One calls sometimes, since glass and resins are at the end of the above sequence, the one electricity glass-, the other resin-electricity.

Both charged states occur simultaneously and are mutually opposite. Depending on its state of charge, each of the rubbed together bodies attracts or repels according to its state of charge an electric pendulum - but only after the bodies have been separated. Both bodies do not move the pendulum, if they are in contact.

A shellac stick with a flannel cap over one of its ends do not display alone or in contact any trace of electricity, unless they have been rubbed against each another. Moreover, if you turn the cap on the stick with friction, the system displays no sign of electricity. However, if you then separate them, they are strongly and mutually oppositely electric (Faraday ).

Thus, the two electricities, which have arisen simultaneously, cancel each other by their action, whence we conclude: Their action is mutually opposite, but their amount is equal, they face each other like the two quantities +E and -E. You say: The two bodies together form an unelectric (neutral) body. A comparison will explain the process of electrification: If you pump air from a closed vessel (at atmospheric pressure) and place it into a second such vessel (at atmospheric pressure), you take from the one vessel as much air away as you place in the other vessel, and in each of them on their own you generate the external atmosphere in face of a changed state of pressure. If you now reconnect the two vessels, they do not display together any difference, neither with respect to each other nor to the environment. A corresponding conclusion applies to bodies, which are in touch with each other and carry opposite electric charges (the shellac stick and flannel cap). Electricity behaves in this respect like air; it is neither generated nor destroyed, it is only displaced from one body to the other*.

* Electricity has indeed a corpuscular character as their exist positive and negative electric particles (elementary particles). They do not only differ from each other by their signs, but also differ like two different chemical elements. They are present in every particle of matter. If such a particle contains equally many positive and negative elementary particles, it is uncharged. If you remove from it positive particles, so that the negative particles are more numerous, it appears to be charged negatively (otherwise positively charged). You should conceive this accordingly: As you rub the glass with silk, the elementary particles separate from each other, the positive ones stick to the glass, the negative ones to the silk.

What is to be explained by the above comparison and what experience tells us over and over again is the fact: It is impossible to generate the one state of charge without simultaneously provoking an equal, oppositely directed state. You express the contrast of the two states of charge by calling the one positive, the other negative, and correspondingly denote them by +e and -e. Traditionally glass electricity is positive, resin electricity is negative. In summary, we have:
1. Two substances which are rubbed against each other become electric.
2. There exist two kinds of electricity: glass- and resin-electricity, called positive and negative electricity**.
3. Both electricities arise simultaneously and in equal amounts; the one body carries positive, the other negative electricity. There exists a law (
Coehn), obeyed by the leading sign of the charge. We only refer to it here, because it involves the concept of the constant of di-electricity (DC): Substances with larger DC become positively charged as they touch substances of smaller DC.
4.
All bodies rubbed in pairs have similar behaviour.
5. Electricities of different leading signs attract, those of equal signs repel each other.

**Electric figures (Fig. 426) display a difference between positive and negative charge at charged locations of an insulator ( Lichtenberg). If you scatter over charged locations a mixture of sulphur flowers and meninges, passing it through a cotton cloth - when the sulphur powder becomes yellow, the meninges powder red - the positively charged places become yellow, the negatively charged ones red; in fact, the positive ones form starlike branched figures, the negative ones circles with many sectors. The polar differences of the figures appear to be coherent in contrast to those of positive ions and negative electrons.

Waterfall-, pyro-, piezo- air-electricity

Processes other than friction can also generate electricity. If drops of water fall on to a surface of water, the air escaping from the location of impact is charged negatively, the water positively, whence waterfalls charge the surrounding air, especially at the foot of a waterfall, where the water masses impact with one another and with wet rocks. (Waterfall electricity, Philip Eduard Anton Lenard 1862-1947). If you heat the mineral tourmaline, its surface is charged positively at one end of its axis, negatively at the other end (during cooling, the inverse happens); other hemi-morphic (only such) crystals have the same behaviour (pyro-electricity). Certain crystals - especially quartz - get charged on their surface under pressure and in tension (piezo-electricity)***. However, electricity generated by processes other than friction does not differ from the frictional electricity (Faraday 1833), whence the experience with frictional electricity applies to electricity, generated by any other method.

*** Oscillations of quartz leaves, generated piezo-electricly in a high frequency alternating electric field, have since a few years (in 1935) an important role for wireless telegraphy and a leading role in telephony.

As a rule, during fair weather, an (temporarily and locally varying) electric field exists over Earth's surface and is charged negatively with respect to the atmosphere. However, during fair weather, the atmosphere contains in the lowest kilometres (observations from a balloon) positively charged masses - free space charges. During fair weather, a conductor held upwards (by a kite string or an isolated stretched wire) is charged positively with respect to Earth. Underneath a cloud, which does not discharge rain, there exists, in general, a similar electric field as during a cloudless sky, but it is weaker. Atmospheric precipitation - the extreme cases are thunderstorms - are always charged electrically. This development of electricity is related to the formation and motion of precipitated particles. The more suddenly water steam is condensed, the stronger are the charges. (The origin of atmospheric electricity is discussed under ionisation of gases.)

Conductors and non-conductors

If you rub glass and silk against each other, only those locations are afterwards charged with electricity which actually touched each other. If you replace glass by a metal sphere - which you have to grab - then on the silk only the rubbed part, but on the metal sphere its entire surface is charged. On silk, electricity remains where it was created, while it spreads on metal, whence you say: Metal conducts electricity, silk does not. A substance is called a conductor or non-conductor (insulator), depending on whether it behaves like metal or silk. For example, conductors are metals, carbon, diluted acids, living plants and animals, insulators are air, resins, glass, silk.

An example (Fig. 427) will clarify the difference between conductors and non-conductors: A is a metal sphere, mounted on the (dry) glass bar B, which has been driven into the ground; all of it is surrounded outside by air. Electrify the metal sphere A by rubbing it, when the charge is spread all over its surface. We are dealing here with metal, air, glass and soil. Experience shows that soil is a good conductor. Air surrounds Earth and the metal sphere. If it were a conductor, it would conduct the electricity away, that is, to the soil and spread it all over Earth, that is, it would almost completely remove the electricity from the sphere. However, air is a non-conductor|, whence no electricity is removed from the sphere. The glass bar is also a non-conductor. If it were a conductor, the electricity would be spread all over Earth through it. The electricity remains confined to the sphere - it is insulated. Air, glass and substances, which behave like it, for example, shellac, resin, paraffin, hard rubber are called insulators.

You see that with the aid of an insulator (glass bar) electricity can be confined to a given location (metal sphere); in contrast, a conductor lets you transfer it to other bodies (Earth). An animal's body behaves like a metal bar. If you take the metal sphere into your bare hands and put your feet (bare or even normally dressed) on the ground, the charge spreads from the metal sphere over your body and from there over Earth. You say: The charge flows through the body to Earth or also: The sphere is discharged through the body to Earth (earthed) or also: discharged. However, if you grasp the sphere with rubber gloves, it retains its charge. If you grasp it with bare hands, but your shoes have rubber soles, the charge will spread over your entire body, but not flow away into Earth. (If you want to make a conductor electric, you must not touch it with bare hands, but place an insulator between it and your hands (for example, rubber gloves).

While the human body is a conductor like a metal and rubber an insulator like air and glass, the ability of various conductors to conduct differs very much and so does the insulators' ability to insulate. The section of electricity, which deals with it at rest, is called electro-statics. Only the fact that there exist insulators makes electro-static phenomena possible. For the time being, we will only mention conduction of electricity as a means of bringing electricity, for example, to an electric pendulum or to Earth.

Electroscope and electrometer

So far we have only encountered mutual attraction and repulsion of bodies as observable actions by which electricity displays its presence. Hence, in order to detect electricity and measure the forces between electrified bodies, we start by only using these actions. Moreover, since these forces are usually rather small, you must make the bodies, which are to be moved, sufficiently easily movable, that is, make the instruments for the detection and measurement of electro-static force very sensitive. For this reason and also because they demand expert treatment, such instruments are only employed in laboratories. If an instrument is used for measurements, it is called an electrometer, if only to detect the presence of electricity, an electroscope.

Fig. 428 shows an electroscope, which is sufficiently sensitive for many purposes: Two very light, small spheres with conducting surfaces (mostly made out of elder marrow covered with a layer of gold) in pendulum suspension with a conducting thread, for example, linen. If you link them by a metal wire to a charged body K, the electricity flows from K through D and the linen threads to the balls and charges both of them in the same sense, whence they repel each other. Movement of the spheres is the sign that the body, to which they are connected, is charged. - However, you can also detect whether a body is charged positively or negatively. If you hold it with a known charge, for example, a positively charged glass bar (rubbed with silk) between the pendulums, their mutual distance will increase, if they are also charged positively, and decrease, if they are charged negatively.

The gold leaf electroscope (Fig. 429) is based on the this phenomenon. Two tinsel leaves L, linked with conduction to each other and to the bar W, replace the pendulums. In order to protect them against air currents or unintended electric effects, they are enclosed in a metal casing with windows. The upper side of the casing has a central hole, closed by a piece of amber or sulphur P, which holds W and is isolated from the casing. (In order to stop the electricity from creeping to the casing via the insulator, it must be dry and free of dust.) If the bar W is not charged, the leaves hang freely side by side, if it is charged, they spread apart more or less depending on the magnitude of the charge. You can use such an electroscope for measurements as electrometer by letting the leaves move in front of a graduated arc as in Fig. 430, where the one gold leaf has been replaced by a fixed metal bar D, the other by a very movable strip of aluminium E (Karl Friedrich Braun 1850-1918).

In these instruments, the repelling force acting on the body of the pendulum (elder marrow sphere, gold leaf, etc.) is in equilibrium with the force of gravity. The body of the pendulum rises like in the letter balance of Fig. 84 until the component of the force of gravity (tangential to the path of the body of the pendulum) directed back to the position of rest equals the electrical force away from it. In other words, the electric force is measured by comparison with the gravitational force.

This force is compared directly with the force of gravity by means of weights in the absolute balance electrometer of William Thomson. Its principle is demonstrated by Fig. 431 (Sir William Snow Harris 1791-1867 1834). The fixed metal plate A and the movable metal plate B are loaded, attract or repel each other and deflect the balance from its equilibrium; the weight required to restore equilibrium - also for very large electric forces only a few gram!- measures the magnitude of the attracting or repelling force. The plate B is surrounded by a ring D, which is connected to it by a conductor and forms with B a plate which is as large as the plate A.

Much more sensitive are those electrometers, in which the movable body is suspended by a thread and (attracted or repelled) rotates about this thread and twists it until the torsional elasticity, which tends to restore it, balances the electric force. The oldest instrument of this type is the torsion balance of Coulomb . It is not suitable for practical measurements and has today only historical significance due to the fact that Coulomb employed it to discover the basic law which controls the mutual attraction and repulsion of electrified bodies. In the torsion balance (Fig. 432), the two electrified bodies are two small conducting spheres one of which (m) is fixed, the other (n) is suspended from the end of a shellac bar p by a fine wire d and can rotate in the horizontal plane. The mutual repulsion of the two equally charged spheres twists the wire, clamped at its upper end. You read the angle of twist against a circular scale; it forms the input to calculations. In order to avoid any effect of the housing, you must take the same precautions as with the electroscope of Fig. 429. You must also earth the housing in order to get rid of electric charges on it.

Coulomb's law

Mutual attraction and repulsion of electrically charged masses allow measurement of the forces, exercised by electric charges. We will now return to our introductory reflections.

Glass and silk stick together once they have been rubbed against each other. Work is required to separate them. Consequently, they form, once they are separated, a system which like a stretched spring has potential energy. Its amount is equal to the work, which you had to perform while transforming the system from the initial state into the new condition (stretched spring); the same amount is returned by the system as the bodies separate from each other, follow their attraction and return to the initial state (like a spring being unloaded). The magnitude of this amount depends on the size of the charge of the two bodies as well as on their respective distance. At first, we want to know the forces which two charged bodies exert on each other. For this purpose, we must measure the quantities of electricity, that is, we must define a unit of electricity.

Let there be given two small, perfectly equal bodies which are 1 cm apart. The space around them is free of air (there is no significant difference if there is air !) Let the two bodies be equally charged, so that the force repelling them from each other is 1 dyn, that is, so that in order that their distance of 1 cm remains unchanged, 1 dyn must be applied. You then say of each of the two bodies contains one unit of electricity.

The following gives you an impression of its magnitude: If in Fig. 428 each of the two elder spheres weigh 10 mg, the almost weightless threads are 50 cm long and the spheres are charged so that they are 10cm apart, each of them has a charge of 10 electric units. A glass bar, rubbed with silk, has a charge of many hundreds electric units. By rubbing it with different strengths, you can generate charges of different magnitude.

Coulomb was the first person to determine the force exercised by two charged bodies on each other. He employed for this purpose the torsion balance (Fig. 432) and discovered the fundamental law of Electricity: If one body contains e1, another e2 units, they are separated by air (more correctly, by a vacuum) and their distance is r cm, then the force by which they repel (or attract) each other is: f = e1ˇe2/r˛. This formula does not contain a proportionality factor, corresponding to the gravitational constant K in Newton's law, or it is better to say that we have set it equal to 1 for air (more correctly: For an airless space).

Coulomb's law tells us: The force with which two electrically charged mass points repel or attract each other, expressed in units of force, is equal to the product of their numbers of unit charges, divided by the square of their mutual distance in centimetres. If every body has 10 units and their distance is 2 cm, the repulsive or attractive force is f = 10ˇ10/2˛ = 25 dyn. Repulsion and attraction are indicated by + and -, respectively. The law only applies to electric charges (static charges) at rest. - According to Coulomb's law, the dimension of an electric quantity is [e] = [lengthˇ(force)1/2] = [m1/2 ˇl3/2t-1].

For the sake of simplicity, we have assumed here that the charges are on point bodies; however, in reality, there exist only extended bodies, for which Coulomb has also discovered the law. Work with the rotation balance is aggravated by many disturbances which affect the demonstrative power of the experimental results. Thus, a strict proof of the correctness of this law is obtained by mathematical reasoning associated with another phenomenon (Faraday's bucket experiment).

If only one of the two bodies is a point, the other an extended body, the force must be computed according to Coulomb's formula, each point of the extensive body exerting a force on the point body. - If a conducting spherical surface is charged uniformly with the quantity e, that is, the charge at each of its points is equally large, it exerts on an external point with unit charge at the distance a cm from its centre a force just as if the total charge were concentrated at its centre, that is, e/a˛ dyn. Let the charge of a sphere be 12 unit charges and its radius 1 cm, then there acts on a charged point at the distance of 10 cm from its centre, the force e/a˛ = 12/100 = 0.12 dyn. Similarly, we find: If the point is located at the distances 9, 8, 7, ˇ ˇ ˇ, 2, 1 cm, it experiences the forces 12/9˛ = 0.15, 12/8˛ = 0.19, ˇ ˇ ˇ , 12/2˛ = 3, 12/1˛ = 12 dyn. The lower curve of Fig 436 shows these values.