K2 Electricity

Electric potential

In order to compute the energy (ability to do work) of electric charges at rest, we consider a body K with a positive unit charge, which is somewhere at rest, isolated and far away from other bodies. We now bring a second body K' with a positive unit charge into its vicinity. This requires work as K repels K', both bodies having a positive charge. This work equals the product of the repelling force and the length of the path, over which the force is overcome. We can compute it, because Coulomb's law yields the force. In general, such computations are very involved since the force changes all along as K approaches K'. Hence we will at first confine ourselves to questions of a general type (of fundamental importance!) and only show below, how to perform the calculations in individual cases.

Let the positive electric charge be initially at an infinite distance from the body (so far that the repelling force it exercises on it, vanishes or is like 0. In practice, this distance can be assumed to be infinite.) Take it now along any path to a point P of the electrical field: This action demands the work A. If you now leave the unit charge at the point P alone, in other words, to the unimpeded action of the repelling body, it will be repelled to an infinite distance and in the process it performs the same amount of work A, which was performed earlier. Hence, by taking the unit charge from infinity to the point P - a new position relative to the repelling body - you have provided it with a certain amount of potential energy. You can employ this work relating to the point P as a characterization of the point P of the electric field and say: At the point P of the electric field rules the potential A+, whence you call potential of a point the work, which must be performed while taking the electric unit charge +1 from infinity to the point in the field of the positively charged body.

Realize now: You must always perform the same work while taking the unit charge from infinity to P, irrespectively of the path. In fact, if this work would be larger along the path W1 than along the path W2, then the unit charge would return more work by returning along W1 than along W2. In other words, if you were to take it along W2 to P and then return it along W1, you would receive more work than you have performed, which, however, would violate the law of conservation of energy. Hence the work cannot depend on the path to P, but only on the location of P, that is, at a given point P of the electric field, the potential has always a definite value and this value is unique.

You can move the unit charge - we mean by this a molecule charged with a unit charge* - to the charged body from infinity along infinitely many paths. In Fig. 434, let the innermost curve be the outline of the charged body and the lines leading to it the paths, along which the unit charge can be taken to it. Say, you take it to B, then you must perform a certain amount of work P, that is, at B is the potential P. If you then take it closer, say to C, you must perform more work, and even more work to take it to D. Hence the potential at C is larger than that at B, and that at D yet larger than that at C. If you release the unit charge after having taken it to C, it merely is subject to the repelling force of the charged body and therefore moves again away from it.

* Also in what follows, this is a test body, say, a very small sphere.

If you replace the positively charged body - let us call it K - by a negatively charged body K' and then again bring a positively charged molecule to the edge of the field, K' attracts the molecule towards it. We understand here by edge of the field the border, at which the action of the body K' effectively ceases - but in doing so we remain conscious of the fact that the field really extends to infinity. When the charged molecule can follow without hindrance the force, exercised on it by K', it will now move from the edge of the field inwards (previously, it moved outwards to the edge). In order to return it from the point P of the field to the edge, the attracting force of K' must be overcome, that is work must be performed and indeed more work the further the point is away from the edge. If the molecule is again charged with a charge of +1 unit, this work is exactly the same as the work to be performed, in order to bring the molecule from the edge to the point P, if K' were charged positively; it was called the potential of the point. The contrast between the work, which we perform in each case, is the same as if we compress a spring the one time (overcoming the repulsion between the body K and the molecule), the other time (overcoming attraction) extend a spring. The charged molecule manifests the contrast between the two cases in that, left to itself at some point P of the field, in the first case it moves to the edge of the field, in the second case moves in the opposite direction. Relative to the point P, we express the contrast by calling the potential in the first case positive, in the second case negative.

However, somewhere between + and - lies zero. What is the potential zero? Answer: The potential of Earth. Earth is a conductor. If electricity is taken to it, it gets charged, whence it must, like every charged body, attract or repel other charged bodies, that is, have a potential. Since it is immensely large, its potential remains unchanged however much electricity it accepts or gives away - comparable to a heat container of immense size, the temperature of which does not change whatever is the amount of heat it takes in or loses. That is why you employ Earth's potential as zero just as you use the temperature of melting ice as zero without implying by this that the temperature of melting ice is not a temperature nor Earth has no potential. Earth's potential is used as marker of potential: We call a potential positive, if it lies above, negative, if it lies below it.

How do you discover whether the potential of a point lies above or below that of Earth? Similarly, how do you discover whether the temperature of a heat source lies above or below that of melting ice? If you place the metal sphere for its examination into a mercury bath at the temperature of melting ice and heat flows from the sphere to the mercury (as you conclude from the rising of a thermometer in the bath), then the temperature lies above 0º, and if there is no transport of heat, the temperature of the sphere is equal to that of melting ice. It is quite similar in the case of electricity: It flows automatically only from a higher to a lower potential; on this fact is founded our examination of whether a given potential lies above or below that of Earth. We have instruments which indicate whether in a wire, which conducts electricity between two points, electricity flows or not, that is, we can find out whether the potentials of the two points differ or are the same; the instruments also shows the direction of the flow of electricity, that is, which point has the higher potential. Such an instrument also indicates whether the potential of a charged body of a point in a field lies above or below that of Earth. However, the potential of a given body is only rarely of interest with respect to that of Earth, as a rule, only with respect to that of another body or point in an electrical field, because we are always only concerned with interactions between charged bodies, one of which may on occasion be Earth. During such measurements, you use the potential of one of the two bodies as zero and measure how much it lies above or below that of the other body. It is somewhat like the case when we are only interested in the temperature difference of two bodies. As a rule, the temperature of a room is only of interest relative to that of our body, that is, we are interested in the temperature difference between our body and the room. We find its numerical value via their relationships to 0º, because that is the way thermometers work. However, differences in the potentials between two points can be measured directly by connecting the points with each other via an electrometer. In this way you discover the difference of the potentials, which they have relative to Earth. You use instead potential difference just potential or also, if the electricity is set in motion, electromotive force (EMF).

Unit of potential difference

In order to state at a given location the measure and number of a potential above or below that of Earth, you employ the unit potential. It is for measurements of potentials what one degree is for that of temperature. The potential is work and work is measured in erg. We now define with the aid of the concept of work the unit of the electrostatic potential: Let there be somewhere an isolated, charged body; if the work 1 erg is required to bring a molecule, charged with unit electricity, from Earth to this body, its potential lies by one unit electrostatic potential above that of Earth; the body has then the potential one. In practice, you employ for measurements of potentials and potential differences 1/300 of this unit; it is called 1 Volt, whence the definition is: 1 Volt = 1/300 the electrostatic unit potential.

Practical examples: The potential difference (EMF) between the poles of a galvanic element is 1 - 2 Volt. In order to make electric incandescent lamps glow, the end points of their wire must have a certain potential difference: Lamps using the electricity of large scale networks are mostly such that they require a potential difference between 200 and 240 Volt. In order to drive an electric tram, their rails and the overhead wire must have a potential difference of about 500 Volt.

All instruments for the measurement of potential differences and direct indication of numbers of Volt are called Voltmeters. Some of them employ the electrostatic attraction or repulsion between charged bodies like the already discussed electrometers. Also the quadrant electrometer becomes a Voltmeter, if its scale is calibrated in Volt. We will describe roughly how this is done: Two oppositely charged, neighbouring bodies attract each other. The magnitude of the force of attraction depends on the magnitude of the potential difference between the two, their form, their size and their relative position. If they are two parallel plates like A and B in Fig. 431 and you know their sizes and distance, you obtain from the theory the relationship of the attractive force to the other quantities. Let the plate B have 100 cm² and the distance between A and B in the equilibrium position of the balance be 0.5 cm. If you then charge A and B so that B sinks and you must place 721 mg* on the right hand side scale dish, in order to return the balance to equilibrium, then the potential difference between A and B is 2000 Volt. In order to calibrate the electrometer's scale, you now connect its housing to the one, the aluminium leaf to the other parallel plate and when the balance has returned to equilibrium mark on the scale 2000 Volt

Equipotential Surfaces. Lines of force

As you find out, whether the potential at a point lies above or below that of Earth, you discover that many points in a field (Fig. 434) have the same potential as the point B, that is, many points can be reached by the same effort P. If all these points are linked, they form a surface, which surrounds the conductor like a shell; similarly, you find a surface, all points of which have the same potential as C, etc. Such surfaces are called equi-potential or level surfaces. Also, the surface of an isolated conductor is a level surface, since, according to our assumption, the electricity on it is at rest. Hence all points of its surface must also have the same potential, because otherwise the electricity would flow from the points of higher to those of lower potential.

Level surfaces enclose each other and the conductor like the layers of an onion; they are only mathematical concepts, but with their aid we can understand better certain processes in an electric field. Consider first several general, geometrical properties, relating to the direction and magnitude of an electric force. Let the charged point body at D' (Fig. 434) move on its own. It then moves to a point of lower potential, that is, it leaves the level surface through D' and moves outwards away from the conductor. But in what direction? It aims at any point of that level surface, which is the neighbour of D' in the outwards direction (in Fig. 434, for the sake of clarity, it is substantially away from D''). But at which point does it aim? At a or at b or which other point? As it is freely movable, it moves naturally in the direction of the force, which at D' acts on it. This force only acts between points with different potentials. Hence it can only act at a right angle to the level surface. A force, directed at an angle to the potential surface, would have a component tangential to it (which joins points of equal potential) and one perpendicularly to it - this one alone is active. In other words: The path of the point-body is everywhere at right angle to the level surface on which the point happens to be. Fig. 434 shows such paths. Everyone indicates simultaneously at each of its points (by the tangent) the direction of the electric force, whence it is called a line of force. You can even make lines of force visible, as will be described below.

What is the size of the electric force perpendicular to a potential surface? In order to discover the force, which drives a charged molecule from D to C, we return to the definition of the potential. Let PC be the work to be performed in order to move a molecule, charged with unit electricity, from infinity (more simply, from the edge of the field) to C, and PD the larger work, in order to move it from the edge to D. (Hence PC and PD are the potentials at C and D.) In order to bring the molecule after its arrival at C to D, we must therefore in addition to the work PC perform so much work that PC becomes PD, that is, we must do the work PD - PC; the path along which this work is performed is of no consequence. The same work PD - PC is now done by the electric force on a molecule with unit electric charge as it is driven from D to C. If it has e units, the work performed by the electric force to take the molecule from a location with potential PD to one with potential PC is e times as large, that is, e·(PD - PC).

Once you have found the entire field of level surfaces and lines of force, as in Fig.434, the field is recorded, say, topographically. For example, for the point F, the direction of the line of force through it indicates the direction in which the charged point will move. Moreover: If we imagine the level surfaces in Fig. 434 recorded in such a way that the values of the potentials differ by equal amounts from surface to surface, you will understand that a molecule, in order to cover the same potential difference, need only cover shorter distances when near the conductor than when it is further away from it. On a map, this would mean that the gradients differ at different locations.

If you compare a charged conductor with a source of heat, the level surfaces are matched by the isothermal surfaces surrounding a heat source: There corresponds to each surface a definite temperature, for each of its points the same, but from surface to surface another temperature; on surfaces closer to the heat source, it is higher than on those further away; lines, which are perpendicular to each surface, tell at each location the direction of the heat flow and the distance (measured along this line) between two of them, between which there is a temperature difference of 1º, measures the gradient.

Examples of lines of force

It is quite difficult to find the level surfaces and lines of force in particular cases. We will only explain their form by means of two simple examples.

Let the conductor be a positively charged sphere (Fig. 435) and the field around it extend to infinity. We approach it with a positively charged molecule radially as far as P. We must then perform work, the magnitude of which is measured by the potential at P. We would have had to perform the same work, if we had taken the molecule to the conductor along another radius to the same distance. This means: The same potential, which applies to P, applies to all points which have the same radial distance from the sphere as P, that is, lie on the spherical surface about C with radius CP. This surface is the equi-potential or level surface. Obviously, every spherical surface about C is such a surface. But on each of them the potential differs: On the surface R, it is smaller than on the surface P, but on the surface Q it is larger than on the surface P, since less work is required to take a molecule to the distance CR than to the smaller distance CQ from the centre of the sphere. The lines of force are equally clearly laid out: They are perpendicular to the level surfaces - here spherical surfaces; therefore the lines of force are the radii of the spherical surfaces.

How large is the potential at a given point? Let e electricity units be distributed uniformly over the surface of a sphere. Then a computation tells us that the potential at a point of the field, the distance a of which from its centre is larger than the radius of the sphere, is e/a. The meaning of this number is: In order to bring a molecule, charged with the positive unit of electricity, from an infinite distance from the sphere, charged with e positive eletricity units, to the distance a from the centre, you require the work e/a erg. If, as earlier, the charge is e=12 electricity units and the radius of the sphere is 1 cm, you must perform the work 12/10 erg while taking the molecule to 10 cm from the centre of the sphere, that is, the point which lies 10 cm from the centre of the sphere has the potential 12. Similarly, we find that at the

 distance of 9 8 6 4 3 2 1 cm from the sphere's centre the potential is 1.33 1.5 2 3 4 6 12

Two equally strongly, oppositely charged bodies A and B are of special interest; their fields intercept each other. If the amount of electricity is known, you can compute for every point in the field at given distances from A and B its potential in the field composed of the two fields.We will now perform the calculation and construct the potential surfaces. Place a horizontal plane through A and B - the plane of the drawing of Fig. 437. It intersects the field as well as the potential surfaces, whence there arise certain curves - the solid curves 1, 2, 3, etc. All the points on 1 have the same potential, similarly those of 2, etc. If positively charged molecules travel from A, they will move away from A, the point with maximum potential, to points of lower potential until they arrive at the point of minimum potential, the point B; in doing so, they move along the lines of force - the dotted lines of Fig. 437 (they intersect the individual equip-otential curves at right angles).

You can make these lines of force visible. Let A and B be small steel spheres, fitted into a (very clean and dry) mirror glass plate and linked to an electrifying machine. Charge them to a corresponding high potential difference and cover the plate with very fine, dry gypsum powder. If you then shake the powder by gently knocking against the plate, the gypsum crystals arrange themselves along lines similar to the dotted lines of Fig. 437 (magnetic lines of force)..

We have only spoken of positively charged molecules, however, a negatively charged molecule, starting from B or taken anywhere in the field and then left to itself, moves naturally along the same lines of force, but in a direction opposite to that of the positively charged molecule; for negatively charged molecules, the largest potential is at the negatively charged body B; it decreases along the lines of force towards A.

Since a charged body moves always from a higher to a lower potential (downhill), you know now the condition under which two charged bodies move towards one another or move away from one another. Let A and B in Fig. 437 be again two equally charged molecules, say, positively charged. In order to bring a molecule, charged with 1 electric unit, to the body, you must obviously, whether you do so from y or y', perform more work than from x or x'. Hence follows: The potential is largest between A and B, it grows in the direction of x and x' towards the two bodies. If you make A and B sufficiently easily movable and leave them to themselves, they will move, since they then move downhill towards x and x', whence they move away from each other - we say that they repel each other. If A and B have opposite charges, the potential values of both the fields around A and B decrease, but both move most strongly towards the centre between A and B; on the line yy', the potential is 0, which means that the fields drop towards this line much more strongly than outwards. If you make again A and B sufficiently movable, both of them will move there, and we say: They attract each other. - A and B behave like two masses, which are placed on a curved track (Figs. 438 a, b) and then are allowed to react to gravity: Both of them move downhill, the one time away from each other, the other time towards each other.

Electrification by induction

Before Faraday, the fact that two bodies move towards or away from each other due to their electrification was viewed as an action at a distance in which the medium between the two bodies did not participate. This view was supported by the fact that one only had to bring an electrified body near to a not yet electrified, easily moved body, for example, one in pendulous suspension, in order to move it. The observation (Thales of Miletus 640-550 BC) that amber, when rubbed with a dry cloth, attracts almost weightless particles like bits of cork, is considered to be the longest known electrical phenomenon.

Accordingly, an electric body seems even to act on a not electrified body at a distance. However, the motion actually takes place as follows: At first, the not electrified body is also electrified, namely by the approaching electrified body - one says by induction - and then both attract each other. Thus we have the stages: 1. Electrification as action at distance and then 2. Mass motion as action at distance. Fig. 439 shows a basic experiment. An uncharged, isolated conductor A, a brass cylinder on a glass foot - at its ends electrified pairs of pendulums - is taken to the charged sphere B. You then observe:

1. Both pendulum pairs spread out, that is, both ends of the conductor A are charged. 2. The pair further away from the sphere indicates presence of the same type of charge as that of the sphere, the pair closer by an opposite charge. In brief: The conductor A carries at its ends opposite charges. 3. The spreading of the pendulums becomes smaller, the closer they are moved to the centre of the cylinder and vanishes at certain points of the cylinder. The totality of these uncharged points around the centre of the cylinder forms the neutral line. 4. If you remove or unload the sphere, the pendulums collapse, the cylinder becomes again unelectric, whence the two opposite charges had the same size. 5. If you discharge the cylinder to Earth at either end, the pendulum pair at b collapses, that is, its charge, which is equal to that on the sphere, vanishes. The other charge remains; it is bound by induced electricity. 6. If, after discharging the cylinder, you remove the sphere first of all, the pendulum pair b spreads again, and indeed with the same charge as the pair a. Hence now the entire surface of the cylinder is charged oppositely to the charge on the sphere. 7. If several conductors are lined up (Fig. 440), each behaves like that next to the sphere.

Induction also occurs, if you place between the induced body e and the induced body ab a glass plate d (Fig. 442). In fact, it occurs through every isolated body, be it solid, fluid or gas, that is also through the atmospheric air.

If you electrify a glass sphere M positively and then take it close to an unelectric, suspended, small body N, it becomes to start with electric by induction. The charge of the glass sphere attracts more strongly the negative electricity a of the induced body due to its shorter distance from N than repelling the further away positive charge b; this is why the glass attracts the body. During the following contact, a corresponding quantum of the positive charge of the glass sphere neutralizes the negative charge of the body. The excess positive charge on the glass has now only to deal with the positive charge of the induced body, that is, it repels therefore the body ab. You can see this attraction and subsequent repulsion when you rub sealing wax or hard rubber with wool and then bring it close to paper clippings or similarly easily moved particles.

Density of electricity

The fact that the electric pendulum (cf. 3. above) does not spread equally strongly at all points of the cylinder indicates that the charge is not the same at all points. It is largest at the ends of the cylinder, zero on the neutral line and has intermediate values in between. In this sense, you speak of density of electricity at a point. Despite of the variability of the density, the electricity is at rest on the surface of the cylinder after the positive and negative electricities have separated; this is a proof that at all points of the surface the potential is equally large. At first, this circumstance comes as a surprise: For example, the point B in Fig. 439 above, although the density of the electricity at it vanishes, is to have a non-zero potential, that is, it is to demand work to bring a molecule, charged with a positive electric unit, into its vicinity, although it does not hold a charge. You should take into account the fact that its neighbours are charged, whence they repel molecules and themselves demand work as the molecule approaches P.

In general, also on a segregated, charged body, the electricity density differs from point to point. The shape of the body is decisive: A sphere has everywhere the same density on its surface, a cylinder has larger density at its ends than in its middle, a disk's density is greater at the edges than at the centre of its faces, a cone's density is stronger at the rim of its mantle than on its sides, but is greatest at its tip. In general: The electricity density on a body is greatest where it has the largest curvature.

A sharp point occupies a special position. Due to the large density of electricity at a vertex, the air there conducts, whence electricity passes directly on to the air molecules, which then, repelled by the equally charged tip, move away. Their positions are occupied by other molecules, so that the cusp loses all the time electricity and maintains around it motion of the air. This air circulation can become a distinct wind (Fig. 443a). However, a vertex also charges. If you take a charged, pointed body A (Fig. 443b) very close to a charged body B, the stream of air discharges its charge on to a body without charge, so that A is unloaded, B is charged. In contrast, if you take a pointed body without charge A' close to a loaded body (Fig. 442 c), negative and positive electricity is generated by induction. Negative electricity flows from the point to the body B' and gradually unloads it; in the end, there is only positive electricity on A', that is, it is as if the charge of B' were simply transferred to A'. You say: The vertex has sucked in the charge. The suction action of a sharp point supports also the action of lightning rods. The suction is so strong that it is occasionally employed technically. For example as follows: You can charge with electricity, generated by rubbing of a glass plate, another body, if you take it away from the glass plate to the body, as soon as the electricity is formed. You employ the method of John Tyndal 1820-1893 (Fig. 444). Attached to the silk R - the rubbing cloth - is a small copper or brass strip P. During rubbing (Fig. 445), the side facing the glass is covered with fine needle points, so that the glass tube is surrounded by a ring of spikes. As you rub with the silk cloth, the ring of spikes glides all the time on that part of the tube to and fro, which had been touched by the silk and just been separated, that is, it has been charged positively. The spikes suck in the positive electricity, which reaches B through the wire W . (Application in electrical machines )

Bondage and re-bondage of Electricity by induction

Your first impression is that also electrification by induction is an action at distance. But if the charge on B (Fig. 439) really acted on A without mediation, that is, A charges without participation of something else but for A and B, it would have to be immaterial what fills the space in between them. But the medium between them has a very important role. In order to understand this, we return to the earlier discussed phenomenon 5.

Let the negative charge, induced on the body A by the positively charged sphere B, be so strongly bonded, that it does not even depart as A is earthed, that is, only its positive electricity leaves. We will now focus our attention on this bonding of electricity by induction.

Bonding is always reciprocal. Hence induced electricity influences also the electricity which induces. The force, which the induced conductor exerts outside, for example, the repulsion of +1 unit of electricity, which is brought near it, becomes thereby much weaker than it was initially. In other words: Its potential has decreased. It must again accept electricity before its potential returns to its initial value; it thus becomes a collection apparatus (a condenser): Let a source of positive electricity be kept throughout (by any means whatever) at a constant potential, also when it loses electricity. Connect the conductor A to it (Fig. 446); then positive electricity flows to A through the conducting connection until A has the same potential as the source of electricity. Now let A approach the conductor B. The positive electricity on A binds the negative one on B; we now earth the positive charge. Since a part of the positive charge is re-bonded to A, the potential of A drops and again new positive electricity can flow to A. The newly entered electricity generates again in B negative electricity to one side and repels positive electricity to the other side. If this repelled electricity is again earthed, the process of bondage and re-bondage is repeated. The potential of A sinks again and A must take in again electricity, in order to raise its potential to the initial level.

However, this cannot continue indefinitely. Not all of the electricity of A becomes outwardly actionless by re-bondage - only one part. The remainder stays free, whence during every new connection of A to a source of electricity the amount of free electricity on it increases and eventually A attains its former potential, although it binds the electricity of B. Then A holds more electricity than before, although its potential is the same. If you move again B to a larger distance from A, the hereto bonded (or better: re-bonded) electricity is freed and the potential of A increases. In this manner, a conductor can be charged to a potential much higher than that of the source of electricity, which causes the charge.

For example, this method is employed, in order to reinforce the potential in the gold leaf electroscope (Fig. 447), which otherwise would not be indicated at all or only vaguely. You fix to the bar l with the gold leaves the metal plate N, cover it above with a layer of varnish and place on top of it a second metal plate M with an isolated handle. You then connect N to the source of electricity and earth M (Fig. 447 left hand side). You have then the set-up of Fig. 446, which explains the bondage and accumulation of electricity. Here N corresponds to the conductor A, which is linked to the source of electricity, M to the conductor B, in which the electricity is generated by induction, in spite of its being earthed, and the varnish layer between N and M to the layer of air between A and B. If you now separate N from the source of electricity and take away M, the entire electricity linked in N is freed and acts on the gold leaves the more, the larger is the area of the two metal plates and the thinner is the layer of varnish.

Dielectric as bearer of the electric field

If the plate A in Fig. 446 is loaded to a given potential V, while only air separates it from B, it accepts a certain amount of electricity. If you then fill the space between it and B with paraffin or glass or any other insulating substance, it will accept a larger amount of electricity than before, in order to attain the same potential. These observations guided Faraday away from action at a distance of electric forces to new views of the nature of induction.

He started from his insight that a magnetized bar, which is broken into two pieces, always yields two new magnets, each with a North pole and a South pole (Fig. 448). You can conceive that the entire magnet NS consist of small magnets ns, whence the magnetisation of a piece of iron is eventually reduced to its single molecules. Faraday then assumed that due to the electrification of the conductor there arises in the bounding insulator- he calls it dielectric - an electric state, because there form similarly in the molecules of the insulator positive and negative poles, which on their part act on the adjoining conductor (Fig. 449).

Let A be a positively, B a negatively charged conductor and ab a row of molecules of the insulator between A and B. Once the poles in the molecules have formed - Faraday calls this state dielectric polarization - pairs of neighbouring molecules in the same row turn towards each other opposite poles and attract each other and the ends a and b attract A and B. Thus, as a result of its polarization, the rows of molecules ab form of a band, which tends to contract and bring the electrified bodies A and B closer together; every other row of molecules between A and B does the same. Hence there exists a tendency to contract in the direction AB.

The state of tension, into which an insulator enters, is a main property of the electric field. The lines, along which the polarized molecules of the insulator contract each other are nothing else but the lines of force, along which a freely movable, charged molecule moves in an electrical field. As a rule, these lines of force are not straight, but more or less curved. Moreover, it is of no consequence whether the space between the two conductors is occupied by air or another (solid, fluid or gaseous) insulator. All these ideas took Faraday away from the concept of direct action of electric forces at a distance; he replaced this concept by a theory, according to which action of a force is transferred by dielectric polarization of the intermediate medium. He employed the words:

"Here the most important among the deductions from the concept that induction is a molecular process is the suspected action along curved lines, for if this could be uniquely established, I cannot see how the old theory of sole action along straight lines at a distance could be maintained or how the conclusion that ordinary induction is an action between adjacent particles can be rejected." Moreover, he wrote: "One can conceive by means of lines of force the external force, which starts from an electric body and reaches into the distance. The lines or the forces, which they represent, remain conserved as long as they are inside of or penetrate an insulating medium. They propagate until they encounter a conducting substance, on which they excite an equally large state, which is opposite to that of their source and of equivalent degree, and in this way their insulation finds a border or they continue, if no such body is present."

Faraday proved over and over again by new facts: During polarization, the dielectric is decisive, the conductor has only the role of the border of the dilelectric. Inside the dielectric, the positive charge of one molecule neutralizes the negative charge of its neighbour on the line of force. Only when the dielectric reaches a conductor, the charge is detected - the charge of the conductor. In a line of force, for example, in the row of molecules ab (Fig. 449 above), the starting point on the conductor A and its end point on the conductor B signify charges, and indeed corresponding points.

Modern ideas of the nature of dielectric polarization

Today we view (on the basis of substantially extended knowledge of electric processes) electricity as something corpular; we ascribe to it atomic structure and assume existence of positive and negative elementary particles of a definite size. According to this concept, the positive (negative) charge of the conductor A (B) (Fig. 449) is identical to a layer of positive (negative) elementary particles on its surface . The end points of the lines of force, linking opposite charges, carry accordingly on the one hand positive and on the other hand negative particles. Elementary particles can be considered to be two elements - we denote them by and - with which other elements can bond (some with , others with , for example, the compounds H and K - a hydrogen ion and a potassium ion -, the compounds Cl - a chlorine ion -and write them, in order to distinguish them from uncharged atoms H+,Cl-. etc.), but which can also bond with each other into - a neutral particle.

According to the view of the structure of matter in 1935, its atoms consist of positive and negative elementary particles; an atom is not charged, if the sum of the positive elementary charges equals the sum of the negative ones. However, if the particles are separated from each other, as Fig. 449 indicates (dipole), then there occurs inside the dielectric that state of tension, which we have described above, and on the bounding layer forms a free charge.

Note one more point: The end points of an electric line of force differ physically completely, that is the positive elementary particles are something completely different from the negative ones. This is not so in the case of magnetic lines of force . Their end points - the positive and the negative poles - only differ in that their actions have different signs.