K3 Electricity

Only the surfaces of conductors are charged

Are corresponding points on the surface of a conductor really the starting and end points of lines of force? Does not possibly a line of force arise inside the conductor and end inside another conductor? This question is answered by the fact that a conductor, on which electricity is at rest, is only charged on its surface and not inside it. This is demonstrated very clearly by an experiment of Cavendish 1731 (Fig. 450}. M is an insulated, charged metal sphere, N and N' are hemispherical shells with insulated handles into which M fits. If you place N and N' over M, so that they form a sphere as a metal skin and then remove again N and N', M is unloaded and the charge on N and N' equals the initial charge on M. Fig. 451 shows a similar set-up, except that the charged sphere is not touched completely by the surrounding skin, but only at one point, where it is connected by the wire M; however, the result is the same.

Faraday has made an experiment at a much larger scale. He built a hollow cube, 12 ft long, covered its sides with a good conductor, insulated it from Earth and gave it a very large charge: "I placed a very sensitive gold leaf electrometer inside the cube and charged the system several times consecutively and strongly from outside; however, neither during charging nor after discharging, the elctrometer nor the internal air displayed the least trace of electricity. - I went inside the cube and stayed there with burning candles, electrometers and all other apparatus for testing electric phenomena without being able to detect the least effect on them nor any special phenomenon, although the outside of the cube was the entire time charged strongly and large sparks and fans of sparks were shooting from its external surface." (Exper. Res. 1173, 1174).

Faraday's bucket experiment. Electric shielding action

Faraday's bucket experiment is especially convincing. (Fig. 452). A is an insulated metal container, free from electricity - a bucket -, B a fitted metal lid, suspended from an insulating string, E a gold leaf electroscope and C a metal sphere which hangs insulated from B. For example, you charge C positive. If you then place the lid on the vessel, so that C is inside a closed space without touching the walls, the vessel A gets charged positively by induction, the electroscope indicates a positive charge. If you now discharge the outside, the leaves of the electroscope collapse; however, if you withdraw the sphere, they spread again, but now with negative electricity, and indeed equally large as before with the positive charge - it is a proof that the two charges, produced on A by induction, are equally large. If you now remove also this charge and place the lid with the sphere on the vessel, so that E indicates again a positive charge, but lower the sphere C (by the thread which passes through a small opening in the lid) on to the bottom of the bucket, so that it gives electricity to the bucket by conduction, it will be totally discharged when you extract it. - However, while the sphere touched the bottom of the bucket - and this is the important point - the spreading of the electroscope leaves remains unchanged. Hence the negative charge inside is equal to the positive charge of the sphere - however, the positive charge on the outside is also equal to the negative charge on the inside, whence it is also equal to that of the sphere. You can therefore view the charge on the outside of A as being the initial charge on the sphere C. While touching the bottom of the bucket, the complete charge of the sphere spread over the surface of the bucket and its inside became completely free from electricity.

Because a charged conductor is only charged on its surface, a line of force can only begin or end there. This is the answer to the questions posed above. - However, corresponding ends of a line of force can never lie on the same conductor, on which the electricity is at rest, because the potential has along a line of force different values, that is, the electricity cannot be at rest. A conductor, which is placed into an electric field like, for example, the sphere K in Fig. 453, interrupts the lines of force which pass through the field. If it is a hollow sphere, a body inside it is protected against the effect of the field, you say: It is shielded (shielding action of a conductor).

The fact that a conductor carries its load only on its surface allows you to derive strictly mathematically Coulomb's law, which is very difficult to prove experimentally. In fact, if the force, which two electric charges exert on each other, were not proportional to the square of the distance between them, but proportional to another power of the distance, an exclusive distribution of charge over the surface would be impossible. Even if the power differed from 2 by a small fraction of 1%, this fact can be established experimentally in the described manner.

Dielectric constant

A dielectric intermediates by its polarization interaction between two charged conductors. Interpreted according to Faraday, the electric field infiltrates the dielectric, which is internally polarized and charged on its boundaries. The thinner the layer of the dielectric, the closer are the charges interlinked and the smaller is their interaction wit the outside. For example, if you rub glass and silk together and leave them in contact with each other, they do not at all affect an electroscope; only after they are separated, each of them acts on the electroscope and the more strongly, the further away it is from the oppositely charged body.

You will understand the role of the dielectric in the charging process, if you arrange the interacting bodies as is shown by Fig. 446 and then increase and decrease the space in between and replace the air by another dielectric. Faraday was also the first person to investigate the effect of different dielectrics non charges . He employed two, concentric, spherical metal shells A and B, connected the internal shell A to a source of electricity and earthed the external shell B. He filled the space C in between with the substance to be tested (insulator) and measured the amounts of electricity required to charge A to the same potential. The following numbers indicate how much larger is the quantity of electricity which A accepts at the same potential as you replace the air in C by another insulator; they are called the dielectric constants of the respective substances. We have set here arbitrarily that of air equal to 1:

How much electricity is accepted by the apparatus, if the space C is a vacuum? The experiment yields only a very small difference between air and a vacuum. If you set the dielectric constant of the vacuum equal to 1, that for air is 1.0006. Much more important is the experience gained by the experiment that electric forces act also through a vacuum. An action without an intermediary contradicts our physical concepts. Hence we assume that there exists a medium - ether- which is present in a vacuum. Its existence is also indicated by other physical facts, especially by the propagation of light through empty space. According to Faraday, the ether intermediates by its polarization the apparent action at a distance and the medium in between has only the role of affecting the ether differently strongly. This explains that different materials have different dielectric constants.

Condensers

Fig. 446 shows a condenser. For practical purposes (especially for wireless telegraphy and telephony), a condenser is given a form so that it can accept the largest possible quantity of electricity; it is best of all to bring two conductors with large surfaces as close together as possible. Also the nature of the isolating layer in between has a considerable influence. Fig. 446 and Fig. 455 present two types of condensers - Riess' apparatus and a Leyden Jar. In both instruments, you earth one conductor and connect the other to a source of electricity; the conductors are relatively thin metal plates. They differ from each other in that in Riess' apparatus the conductors are separated by air, in the Leyden jar by glass. Moreover, in the Leyden jar, the glass is a beaker with both conductors in close contact with the glass. (When producing the jar, you must leave free a rather broad rim of the glass, since otherwise charges creep along the glass and interact.) In order to create a condenser of large capacity, you interlink several condensers: For example, you place large, equally sized glass plates on top of each other and place ain in between pairs of plates small leaves of tin foil, in order not to cover a sufficiently large, isolating section of the glass. Eventually, you interconnect the sheets of foil alternatingly as shown in Fig. 456. Instead of glass ( as dielectric) you can also use paper with paraffin or very thin mica sheets, often even just air. For example, the plates in a condenser of varying capacity are semi-circular metal sheets. The one system (left hand side in Fig. 447) is fixed, the other can be rotated about the axis A, so that you can insert the leaves of the movable system by rotation arbitrarily far into the spaces between the fixed leaves. The further they are inserted, the larger is the capacity.

Electrostatic capacity

All condensers consist of two close to each other conductors with an isolating layer in between them. Hence, two conductors withan isolating layer in between must act like a condenser, for example, a submarine telegraph cable (Fig. 458) . The essential part of the cable, the copper wire A, is surrounded by insulating material B , which is protected against mechanical effects by a metal coating C. Hence the conductor C encloses completely the conductor A and is separated from it by the isolating layer B. Thus, A, B and C are by their arrangement like a very long Leyden Jar, in which A is the internal conductor, connected to a source of electricity, C the earthed outer and B the intermediate isolating layer. The internal conductor transmits the telegraphic signal, whence it is connected to a source of electricity: The external metal cover is earthed or lies in water. Not all of the electricity, which enters A reaches its goal, for it charges by induction the armature C and bonds the charge, but it is also partly itself bonded, that is, the cable charges first itself. Only afterwards will electricity reach the receiving station. That is why the signal arrives there later than it should (in an Atlantic cable the delay is about 3/4 second). This delay occurs with every signal. The time of loading depends on how much electricity is demanded by the copper wire, in order to reach the potential of the source of electricity, connected to it; but it also depends on the ratio of this amount of electricity to the potential, generated by it on the copper wire. This ratio is referred to as the capacity of the cable. In general, you understand by the capacity c of a condenser the ratio of the quantity of electricity e on the conductor to its potential V, while the other conductor is earthed (has the potential zero). The definition is:

capacity = quantity of electricity/potential or c = e/V.

When we speak of the capacity of a condenser, we really mean by this the capacity of one conductor in a given position with respect to the other conductor. If we remove the second conductor to infinity, the (re-bonded) electricity on the first conductor (the condenser) is freed. Hereby rises the potential. Then the denominator in the fraction quantity of electricity/potential becomes larger, that is, the fraction becomes smaller and thereby the capacity of the conductor becomes smaller as the earthed conductor is moved further away from it. Hence the same source of electricity transports more or less electricity through a conductor, depending on its environment. In other words: The same quantity of electricity generates on a conductor a different potential depending on whether there is in its vicinity a conductor or not. Its potential is the largest, that is, its capacity the smallest, if it is by itself; it is smallest, that is, its capacity the largest, if an earthed conductor is closeby, and it lies in between these two values, when the inducible conductor is in its vicinity, but not earthed. You see that not only the actual condensers, but altogether all conductors have capacity. However, for condensers, in general, the capacity is considerably larger than for ordinary conductors. Depending on the dielectric constant, the capacity differs under otherwise equal conditions.

In order to measure capacities, you must have
1. a measure for capacity and
2. methods for their measurement, that is, be able to compare the capacity of a given condenser with one assumed to have unit capacity. The capacity of a conductor is given by the ratio of the amount of electric charge on it to the potential, which it receives by the amount of electricity while its environment has the potential zero. Hence you allot to a condenser the capacity one, which receives from a unit electric charge the unit potential, while its environment has the potential zero.

Unit capacity has - we will not present the proof - a sphere of radius 1 cm, insulated in air. You employ for measurements a unit which is 900 000 times as large, the micro-farad, the millionth part of the Farad. For example, the capacity of a cable or any conductor is a certain number of micro-farads. This is a comparatively large unit: A condenser of the form of Fig. 446, the plates of which are 1 cm apart, and which has 1 micro-farad capacity, would have to have plates with an area of 1131 m²; a piece of cable of the form of Fig. 458, would have to be about 5 km long. A sphere of the diameter of Earth would have a capacity of 700 micro-farad.

In certain cases, you can compute the capacity, for example, that of spherical condensers (Fig. 454) from the radii of the two spherical shells, that of a cylindrical condenser from its length and its two radii. In most cases, you must measure it by comparing it with a measuring condenser of known capacity. A measuring condenser is subdivided into fractions of micro-farad.

Spark discharge

The dielectric between two oppositely charged conductors is in a state of tension. You cannot increase it (by increasing the charge) indefinitely. In fact, if you do so, eventually a spark, accompanied by noise, travels through the dielectric from the one conductor to the other and at the same instant the charge and tension disappear. The return of the particles of the dielectric from the state of tension into its natural state is called tension equalization, the lightening like phenomenon is caled an electric spark and correspondingly the discharge a spark discharge. You can compare the dielectric between the conductors with an elastic separating wall between two rooms A and B, both of which contain initially air at atmospheric pressure. If you suck the air out of A and transport it to B, the separating wall experiences excess pressure from B to A. If you continue the process, the wall suddenly bursts and both rooms return to their initial state.

Maxwell wrote: "The process appears to be analogous to the tearing of a solid body under a steadily increasing load. The analogue is so perfect that we, when we describe the behaviour of substances under the action of an electromotoric force, can employ the same expressions which we apply to bodies under mechanical loads. Hence electromotoric force and electric displacement correspond to ordinary force and ordinary displacement. An electromotoric force, which causes a disruptive discharge corresponds to the failure load."

For example, if the dielectric is a solid substance - glass or resin -, it is penetrated during a spark discharge by a threadlike channel and the heat accompanying the spark leaves behind it a trace of melting, burning or vapour. If the dielectric is a fluid - oil or a gas -, the path taken by the spark closes again and the dielectric returns to its initial state, whence a fluid or also air are in many cases superior to a solid insulator.

You can always cause a spark discharge by increasing sufficiently the tension. The condition under which it occurs depends on the potential difference between the conductors, bounded by the dielectric, and therefore on the nature of the dielectric, its dimensions, moreover on the form of the conductor (effect of sharp points), on the smoothness or roughness of its surface, etc. A discharge can have quite different forms. The discharge of a sharp point in darkness is accompanied by a weak, blue-red light and out of the tip radiates a bundle of glowing lines (bundle discharge, bundle light), this also occurs during St. Elmo's fire. A similar phenomenon occurs during discharges in diluted gases, depending on the degree of dilution and the kind of gas.

Electric friction machine

So far, we only know that friction between two bodies and induction generate electricity. In order to generate it in larger quantities and to be able to handle more readily the parts rubbing each other, they are employed in a electric machine. (It was invented by Guericke 1660. Fig. 459 shows it in its simplest form. The glass disk P and rubbing materials R and R' made out of leather and covered with a substance made out of mercury, zinc and tin are the parts which generate electricity. Instead of holding the glass fixed and moving the rubbing agent, you rotate the disk by means of a crank between the rubbing cloth, pressed hard against the disk. The glass disk, positively charged by the rubbing cloth, approaches during the rotation the combs A and A', which have many fine metal needles, extending to the glass disk. The positive electricity is sucked in by the needles and passed on to the knob K (and from there to the body to be charged). You connect the negatively charging rubbing cloth either to a body to be charged or to Earth. The larger part of the work spent on rotating the disk becomes heat. The work of turning overcomes first the braking of the disk by the rubbing cloth. This part of the work is converted into heat. Next, it overcomes the attraction of the negatively charged rubbing cloth exerted on the positively charged glass disk, which also acts like a brake. In fact, the negatively charged R attempts to turn back the part A of the positively charged glass plate (Fig. 460), which it is just leaving behind and which has still its complete charge (arrow A). However, the rubbing cloth attracts the part B (which has passed most of its charge on to the needles and which is already approaching it) (arrow B). But it attracts A much more strongly, because it has still its entire charge while B has already given away most of it. Hence electrification leaves behind an excess braking action. Only a very small part of the work spent is therefore utilized in the electric friction machine.

Electrofor

Induction machines are much superior to electric friction machines. The electrofor of Alessandro Volta was an incomplete forerunner - essentially only an isolator I, a resin or ebonite disk or such like and a movable metal plate P with an insulated handle R (Fig. 461). It is used as follows: The surface of the resin plate I is charged negatively by friction. When it approaches the metal cover P, the negative electricity acts on the hitherto non-electric lid P by induction, draws from P positive electricity to the side, facing the plate, and bonds it there. If you now take away the negative charge from the lid while it lies on the plate (by touching it with your fingers) and then remove the lid from the region of attraction of the resin plate, the bonded positive electricity is freed. The lid is now charged positively, can pass its charge on to another conductor and can be charged again by being taken close to the resin plate, etc. The supply of negative charge on the resin plate I is not affected by this action, whence you can repeat the electrification of the lid by the resin plate as often as desired and increase the charge of the body. The resin plate charges the metal plate B by induction, the negative charge is earthed; however, the positive charge bonds the negative charge of the resin plate and protects it against dispersion and removal to the lid, touching it. Indeed, the lid does not get charged, as you deposit it on the resin plate and lift it off without touching it.

Electric induction machines

Electric induction machines are very efficient as sources of electricity. We will give details of the machine of August Adolf Kundt 1838-1894, which bridges the transition from the electrofor to the induction machine, although it is not exactly an induction machine. In essence, it consists of a rotatable glass disk A (Fig. 462), an insulated, charged body B nearby in front of the disk, which acts strongly inducing on it and - on the other side of the disk - two oppositely placed sets of metal combs C and D for charging with and sucking off electricity. The negatively electrified body B acts (through the disk) inducing on the comb C and draws the positive electricity into its spikes, while the negative electricity assembles in C'. The positive electricity flows from the comb to the disk, arrives with the rotating disk in front of the comb D, which sucks it off. (Fig. 463).

Fig. 463 explains the machine once more. The disk A of Fig. 460 is here replaced by a (rotatable in the direction of the arrow ) glass bar, bent into a ring. You can thus demonstrate the entire arrangement with inessential changes in the plane of the drawing. B on the outside of the ring represents the negatively charged body (resin plate), C and D inside the ring are the combs. - In order to avoid a misunderstanding of the diagram, Fig. 464 presents the corresponding diagram for the electric friction machine (Fig. 459). In front of and behind the disk now become inside and outside the ring.

The glass disk has here the role of the cover P of the electrofor. But the process is by far superior to that of the electrofor. Since the disk rotates quickly,other points of the disk lie at each instant in front of the inductor B and in front of the comb. Hence there flows at each instant electricity into the combs and at each instant positive as well as negative electricity.

Kundt's machine has much better efficiency than the electric friction machine, but as such a machine it has many faults. Firstly, it can only be used as long as B retains its charge and, secondly, the performance which can be reached with it depends on the magnitude of the potential of B. If it is small, its performance is correspondingly small. Actual induction machines are better apart from this aspect (Holtz 1836-1913). We will refer to Kundt's machine during the following description. Also the side of the disk, which is facing the inductor B, becomes positively electric, indeed so only weakly (outer side of the ring in Fig. 463). Place a non-electric body B' with a tip symmetrically to B and opposite the comb D (Fig. 465): It sucks in the positive electricity, which arrives with the rotating disk. As soon as it has taken in a certain amount, it acts towards the disk and the comb D exactly like B, except that it transports negative electricity to D and induces negative electricity on the side of the disk which faces it. As the disk rotates, the negative electricity of the side of the disk, facing B', now arrives at B. If B has also a sharp tip, it sucks this negative electricity in, that is, it increases - this is the main asset of the induction machine - its own charge and consequently induces more strongly. As the rotation of the disk continues, also B' sucks in electricity, thereby strengthens its charge and besides induces more strongly, etc. In this manner , these actions reinforce each other in turn to a limit, which depends on the conditions of insulation of the machine.

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