The Mathematical Theory of Electricity and Magnetism (5th ed, 1927) — part 2 of 39

13. On shaking up a mixture of powdered red lead and yellow sulphur, the particles of red lead will become positively electrified, and those of the sulphur will become negatively electrified, as the result of the friction which has occurred between the two sets of particles in the shaking. If some of this powder is now dusted on to a positively electrified body, the particles of sulphur will be attracted and those of red lead repelled. The red lead will therefore fall off, or be easily removed by a breath of air, while the sulphur

11-15] The Fundamental Conceptions of Electrostatics 11

particles will be retained. The positively electrified body will therefore assume a yellow colour on being dusted with the powder, and similarly a negatively electrified body would become red. It may sometimes be con- venient to use this method of determining whether the electrification of a body is positive or negative.

14. The attraction and repulsion of two charged bodies is in many respects different from the force between one charged and one uncharged body. The latter force, as we have explained, was known to the Greeks : it must be attributed, as we shall see, to what is known as "electric induction," and is invariably attractive. The forces between two bodies both of which are charged, forces which may be either attractive or repulsive, seem hardly to have been noticed until the eighteenth century.

The observations of Robert Symmer (1759) on the attractions and repulsions of charged bodies are at least amusing. He was in the habit of wearing two pairs of stockings simultaneously, a worsted pair for comfort and a silk pair for appearance. In pulling off his stockings he noticed that they gave a crackling noise, and sometimes that they even emitted sparks when taken off in the dark. On taking the two stockings off together from the foot and then drawing the one from inside the other, he found that both became inflated so as to reproduce the shape of the foot, and exhibited attractions and repulsions at a distance of as much as a foot and a half.

" When this experiment is performed with two black stockings in one hand, and two white in the other, it exhibits a very curious spectacle ; the repulsion of those of the same colour, and the attraction of those of different colours, throws them into an agitation that is not unentertaining, and makes them catch each at that of its opposite colour, and at a greater distance than one would expect. When allowed to come together they all unite in one mass. When separated, they resume their former appearance, and admit of the repetition of the experiment as often as you please, till their electricity, gradually wasting, stands in need of being recruited."

The Law of Force between charged Particles.

15. The Torsion Balance. Coulomb (1785) devised an instrument known as the Torsion Balance, which enabled him not only to verify the laws of attraction and repulsion qualitatively, but also to form an estimate of the actual magnitude of these forces.

The apparatus consists essentially of two light balls A, C, fixed at the two ends of a rod which is suspended at its middle point B by a very fine thread of silver, quartz or other material. The upper end of the thread is fastened to a movable head JD, so that the thread and the rod can be made to rotate by screwing the head. If the rod is acted on only by its weight, the

12

Electrostatics — Physical Prin ciples

[ch. l

condition for equilibrium is obviously that there shall be no torsion in the thread. If, however, we fix a third small ball E in the same plane as

the other two, and if the three balls are elec- trified, the forces between the fixed ball and the movable ones will exert a couple on the moving rod, and the condition for equilibrium is that this couple shall exactly balance, that due to the torsion. Coulomb found that the couple exerted by the torsion of the thread was exactly proportional to the angle through which one end of the thread had been turned relatively to the other, and in this way was enabled to measure his electric forces. In Coulomb's experiments one only of the two movable balls was electrified, the second serv- ing merely as a counterpoise, and the fixed ball was at the same distance from the torsion

thread as the two movable balls. Fig. 2.

Suppose that the head of the thread is turned to such a position that the balls when uncharged rest in equilibrium, just touching one another Avithout pressure. Let the balls receive charges e, e', and let the repulsion between them result in the bar turning through an angle 6. The couple exerted on the bar by the torsion of the thread is proportional to 0, and may therefore be taken to be k6. If a is the radius of the circle described by the movable ball, we may regard the couple acting on the rod from the electric forces as made up of a force F, equal to the force of repulsion between the two balls, multiplied by a cos \Qt the arm of the moment. The condition for equilibrium is accordingly

aF cos \B = k9.

Let us now suppose that the torsion head is turned through an angle 0 in such a direction as to make the two charged balls approach each other; after the turning has ceased, let us suppose that the balls are allowed to come to rest. In the new position of equilibrium, let us suppose that the two charged balls subtend an angle 6' at the centre, instead of the former angle 6. The couple exerted by the toi'sion thread is now k{9' + <f>), so that if F' is the new force of repulsion we must have

aF' cos & = k (6' + 0).

By observing the value of <f> required to give definite values to & we can calculate values of F' corresponding to any series of values of 6'. From a series of experiments of this kind it is found that so long as the charges on the two balls remain the same, F' is proportional to cosec2^#', from which it is easily seen to follow that the force of repulsion varies inversely as the

15, 16] The Fundamental Conceptions of Electrostatics 13

square of the distance. And when the charges on the two balls are varied it is found that the force varies as the product of the two charges, so long as their distance apart remains the same. As the result of a series of experi- ments conducted in this way Coulomb was able to enunciate the law :

The force between two small charged bodies is proportional to the product of their charges, and is inversely proportional to the square of their distance apart, the force being one of repulsion or attraction according as the two charges are of the same or of opposite kinds.

16. In mathematical language we may say that there is a force of repul- sion of amount

cee'

/y*Z

•(1)

where e, e' are the charges, r their distance apart, and c is a positive constant.

If e, e are of opposite signs the product ee' is negative, and a negative repulsion must be interpreted as an attraction.

Although this law was first published by Coulomb, it subsequently appeared that it had been discovered at an earlier date by Cavendish, whose experiments were much more refined than those of Coulomb. Caven- dish was able to satisfy himself that the law was certainly intermediate between the inverse 2 + ^ and 2 — ^th power of the distance (see below, §§ 46 — 48). Unfortunately his researches remained unknown until his manuscripts were published in 1879 by Clerk Maxwell.

The experiments of Coulomb and Cavendish, it need hardly be said, were very rough compared with those which are rendered possible by modern refinements of theory and practice, so that these experiments are no longer the justification for using the law expressed by formula (1) as the basis of the Mathematical Theory of Electricity. More delicate experiments with the apparatus used by Cavendish, which will be explained later, have, however, been found to give a complete confirmation of Coulomb's Law, so long as the charged bodies may both be regarded as infinitely small compared with their distance apart. Any deviation from the law of Coulomb must accord- ingly be attributed to the finite sizes of the bodies which carry the charges. As it is only in the case of infinitely small bodies that the symbol r of formula (1) has had any meaning assigned to it, we may regard the law (1) as absolutely true, at any rate so long as r is large enough to be a measurable quantity.

14 Electrostatics — Physical Principles [ch. i

The Unit of Electricity.

17. The law of Coulomb supplies us with a convenient unit in which to measure electric charges.

The unit of mass, the pound or gramme, is a purely arbitrary unit, and all quantities of mass are measured simply by comparison with this unit. The same is true of the unit of space. If it were possible to keep a charge of electricity unimpaired through all time we might take an arbitrary charge of electricity as standard, and measure all charges by comparison with this one standard charge, in the way suggested in § 8. As it is not possible to do this, we find it convenient to measure electricity with reference to the units of mass, length and time of which we are already in possession, and Coulomb's Law enables us to do this. We define as the unit charge a charge such that when two unit charges are placed one on each of two small particles at a distance of a centimetre apart, the force of repulsion between the particles is one dyne. With this definition it is clear that the quantity c in the formula (1) becomes equal to unity, so long as the c.G.S. system of units is used.

In a similar way, if the mass of a body did not remain constant, we might have to define the unit of mass with reference to those of time and length by saying that a mass is a unit mass provided that tAvo such masses, placed at a unit distance apart, produce in each other by their mutual gravitational attraction an acceleration of a centimetre per second per second. In this case we should have the gravitational acceleration f given by an equation of the form

/-£ (2).

and this equation would determine the unit of mass.

18. Physical dimensions. If the unit of mass were determined by equation (2), m would appear to have the dimensions of an acceleration multiplied by the square of a distance, and therefore dimensions

DT~\

As a matter of fact, however, we know that mass is something entirely apart from length and time, except in so far as it is connected with them through the law of gravitation. The complete gravitational acceleration is given by

where y is the so-called " gravitation constant."

By our proposed definition of unit mass we should have made the value of 7 numerically equal to unity; but its physical dimensions are not those of

17, 18] The Fundamental Conceptions of Electrostatics 15

a mere number, so that we cannot neglect the factor y when equating physical dimensions on the two sides of the equation.

So also in the formula

F=~ (8)

we can and do choose our unit of charge in such a way that the numerical value of c is unity, so that the numerical equation becomes

*=% (4),

but we must remember that the factor c still retains its physical dimensions. Electricity is something entirely apart from mass, length and time, and it follows that we ought to treat the dimensions of equation (3), by introducing a new unit of electricity E and saying that c is of the dimensions of a force divided by E2/r* and therefore of dimensions

MLsE-2T-\

If, however, we compare dimensions in equation (4), neglecting to take account of the physical dimensions of the suppressed factor c, it appears as though a charge of electricity can be expi'essed in terms of the units of mass, length and time, just as it might appear from equation (2) as though a mass could be expressed in terms of the units of length and time. The apparent dimensions of a charge of electricity are now

MWT-1 (5).

It will be readily understood that these dimensions are merely apparent and not in any way real, when it is stated that other systems of units are also in use, and that the apparent physical dimensions of a charge of electricity are found to be different in the different systems of units. The system which we have just described, in which the unit is denned as the charge which makes c numerically equal to unity in equation (3), is known as the Electrostatic system of units.

There will be different electrostatic systems of units corresponding to different units of length, mass and time. In the c.G.s. system these units are taken to be the centimetre, gramme and second. In passing from one system of units to another the unit of electricity will change as if it were a physical quantity having dimensions M^L*T~X, so long as we hold to the agreement that equation (4) is to be numerically true, i.e. so long as the units remain electrostatic. This gives a certain importance to the apparent dimensions of the unit of electricity, as expressed in formula (5).

16 Electrostatics — Physical Principles [ch. i

V. Electrification by Induction.

19. Let us suspend a metal rod by insulating supports. Suppose that the rod is originally uncharged, and that we bring a small body charged with electricity near to one end of the rod, without allowing the two bodies to touch We shall find on sprinkling the rod with electrified powder of the kind previously described (§ 13), that the rod is now electrified, the signs of the charges at the two ends being different. This electrification is known as electriiication by induction. We speak of the electricity on the rod as an induce I charge, and that on the originally electrified body as the inducing or exciting charge. We .find that the induced charge at the end of the rod nearest to the inducing charge is of sign opposite to that of the inducing charge, that at the further end of the rod being of the same sign as the inducing charge. If the inducing charge is removed to a great distance from the rod, we find that the induced charges disappear completely, the rod resuming its original unelectrified state.

If the rod is arranged so that it can be divided into two parts, we can separate the two parts before removing the inducing charge, and in this way can retain the two parts of the induced charge for further examination.

If we insert the two induced charges into the vessel of the electroscope, we find that the total electrification is nil: in generating electricity by induction, as in generating it by friction, we can only generate equal quantities of positive and negative electricity; we cannot alter the algebraic total charge. Thus the generation of electricity by induction is in no way a violation of the law that the total charge on a body remains unaltered except in so far as it is removed by conduction.

20. If the inducing charge is placed on a sufficiently light conductor, we notice a violent attraction between it and the rod which carries the induced charge. This, however, as we shall now shew, is only in accordance with Coulomb's Law. Let us, for the sake of argument, suppose that the inducing charge is a positive charge e. Let us divide up that part of the

ABC C B'A'

( )

Pig. 3.

rod which is negatively charged into small parts AB, BG, ... , beginning from the end A which is nearest to the inducing charge I, in such a way that each part contains the same small charge — e, of negative electricity. Let us similarly divide up the part of the rod which is positively charged into

19-22] The Fundamental Conceptions of Electrostatics 17

sections A'B', B'C, ... , beginning from the further end, and such that each of

these parts contains a charge -f e of positive electricity. Since the total

induced charge is zero, the number of positively charged sections A'B',

B'C, ... must be exactly equal to the number of negatively charged sections

AB, BO, The whole series of sections can therefore be divided into a

series of pairs

AB and A'B' ; BC and B'C ; etc.

such that the two sections of any pair contain equal and opposite charges. The charge on A'B' being of the same sign as the inducing charge e, repels the body / which carries this charge, while the charge on AB, being of the same sign as the charge on i", attracts /. Since A B is nearer to I than A'B', it follows from Coulomb's Law that the attractive force ee/r2 between AB and / is numerically greater than the repulsive force ee/r2 between A'B' and I, so that the resultant action of the pair of sections AB, A'B' upon / is an attraction. Obviously a similar result is true for every other pair of sections, so that we arrive at the result that the whole force between the two bodies is attractive.

This result fully accounts for the fundamental property of a charged body to attract small bodies to which no charge has been given. The proximity of the charged body induces charges of different signs on those parts of the body which are nearer to, and further away from, the inducing charge, and although the total induced charge is zero, yet the attractions will always outweigh the repulsions, so that the resultant force is always one of attraction.

21. The same conceptions explain the divergence of the gold-leaves of the electroscope which occurs when a charged body is brought near to the plate of the electroscope or introduced into a closed vessel standing on this plate. All the conducting parts of the electroscope — gold-leaves, rod, plate and vessel if any — may be regarded as a single conductor, and of this the gold-leaves form the part furthest removed from the charged body. The leaves accordingly become charged by induction with electricity of the same sign as that of the charged body, and as the charges on the two gold-leaves are of similar sign, they repel one another.

22. On separating the two parts of a conductor while an induced charge is on it, and then removing both from the influence of the induced charge, we gain two charges of electricity without any diminution of the inducing charge. We can store or utilise these charges in any way and on replacing the two parts of the conductor in position, we shall again obtain an induced charge. This again may be utilised or stored, and so on indefinitely. There is therefore no limit to the magnitude of the charges which can be obtained from a small initial charge by repeating the process of induction.

This principle underlies the action of the Electrophorus. A cake of resin is electrified by friction, and for convenience is placed with its electrified j. 2

I

18 Electrostatics — Physical Principles [oh. i

surface uppermost on a horizontal table. A metal disc is held by an insulating handle parallel to the cake of resin and at a slight distance above it. The operat >r then touches the upper surface of the disc with his finger. When the process has reached this stage, the metal disc, the body of the operator and the earth itself form one conductor. The negative electricity on the resin induces a positive charge on the nearer parts of this conductor — primarily on the metal disc — and a negative charge on the more remote parts of the conductor — the further region of the earth. When the operator removes his fi] ger, the disc is left insulated and in possession of a positive charge. As already explained, this charge may be used and the process repeated indefinitely.

In all its essentials, the principle utilised in the generation of electricity by the " influence machines" of Voss, Holtz, Wimshurst and others is identical with that of the electrophorus. The machines are arranged so that by the turning of a handle, the various stages of the process are repeated cyclically time after time.

23. Electric Equilibrium. Returning to the apparatus illustrated in fig. 3, p. 16, it is found that if we remove the inducing charge without allowing the conducting rod to come into contact with other conductors, the charge on the rod disappears gradually as the inducing charge recedes, positive and negative electricity combining in equal quantities and neutral- ising one another. This shews that the inducing charge must be supposed to act upon the electricity of the induced charge, rather than upon the matter of the conductor. Upon the same principle, the various parts of the induced charge must be supposed to act directly upon one another. Moreover, in a conductor charged with electricity at rest, there is no reaction between matter aDd electricity tending to prevent the passage of electricity through the conductor. For if there were, it would be possible for parts of the induced charge to be retained, after the inducing charge had been removed, the parts of the induced charge being retained in position by their reaction with the matter of the conductor. Nothing of this kind is observed to occur. We conclude then that the elements of electrical charge on a conductor are each in equilibrium under the influence solely of the forces exerted by the remaining elements of charge.

24. An exception occurs when the electricity is actually at the surface of the conductor. Here there is an obvious reaction between matter and electricity — the reaction which prevents the electricity from leaving the surface of the conductor. Clearly this reaction will be normal to the surface, so that the forces acting upon the electricity in directions which lie in the tangent plane to the surface must be entirely forces from other charges of electricity, and these must be in equilibrium. To balance the action of the matter on the electricity there must be an equal and opposite reaction of

22-27] Theories of Electrical Phenomena 19

electricity on matter. This, then, will act normally outwards at the surface of the conductor. Experimentally it is best put in evidence by the electrification of soap-bubbles. A soap-bubble when electrified is observed to expand, the normal reaction between electricity and matter at its surface driving the surface outwards until equilibrium is reestablished (see below, § 94).

25. Also when two conductors of different material are placed in con- tact, electric phenomena are found to occur which have been explained by Helmholtz as the result of the operation of reactions between electricity and matter at the surfaces of the conductors. Thus, although electricity can pass quite freely over the different parts of the same conductor, it is not strictly true to say that electricity can pass freely from one conductor to another of different material with which it is in contact. Compared, however, with the forces with which we shall in general be dealing in electrostatics, it will be legitimate to disregard entirely any forces of the kind just described. We shall therefore neglect the difference between the materials of different con- ductors, so that any number of conductors placed in contact may be regarded as a single conductor.

Theories to explain Electrical Phenomena.

26. One- fluid Theory. Franklin, as far back as 1751, tried to include all the electrical phenomena with which he was acquainted in one simple explanation. He suggested that all these phenomena could be explained by supposing the existence of an indestructible " electric fluid," which could be associated with matter in different degrees. Corresponding to the normal state of matter, in which no electrical properties are exhibited, there is a definite normal amount of "electric fluid." When a body was charged with positive electricity, Franklin explained that there was an excess of " electric fluid " above the normal amount, and similarly a charge of negative electricity represented a deficiency of electric fluid. The generation of equal quantities of positive and negative electricity was now explained: for instance, in rubbing two bodies together we simply transfer " electric fluid " from one to the other. To explain the attractions and repulsions of electrified bodies, Franklin supposed that the particles of ordinary matter repelled one another, while attracting the "electric fluid." In the normal state of matter the quantities of "electric fluid " and ordinary matter were just balanced, so that there was neither attraction nor repulsion between bodies in the normal state. According to a later modification of the theory the attractions just out-balanced the repulsions in the normal state, the residual force accounting for gravitation.

27. Two-fluid Theory. A further attempt to explain electric phenomena was made by the two-fluid theory. In this there were three things concerned, ordinary matter and two electric fluids — positive and negative. The degree of electrification was supposed to be the measure of the excess of positive

2—2

20 Electrostatics — Physical Principles [oh. i

electricity over negative, or of negative over positive, according to the sign of the electrification. The two kinds of electricity attracted and repelled, electa 3i ties of the same kind repelling, and of opposite kinds attracting, and in this way the observed attractions and repulsions of electrified bodies were explained without having recourse to systems of forces between electricity and ordinary matter. It is, however, obvious that the two-fluid theory was too elaborate for the facts. On this theory ordinary matter devoid of both kinds of electricity would be physically different from matter possessing equal quantities of the two kinds of electricity, although both bodies would equally shew an absence of electrification. There is no evidence that it is possible to establish any physical difference of this kind between totally unelectrified bodies, so that the two-fluid theory must be dismissed as explaining more than there is to be explained.

28. Modern view of Electricity. The two theories which have just been mentioned rested on no experimental evidence except such as is required to establish the phenomena with which they are directly concerned. The modern view of electricity, on the other hand, is based on an enormous mass of experimental evidence, to which contributions are made, not only by the phenomena of electrostatics, but also by the phenomena of almost every branch of physics and chemistry. The modern explanation of electricity is found to bear a very close resemblance to the older explanation of the one- fluid theory — so much so that it will be convenient to explain the modern view of electricity simply by making the appropriate modifications of the one-fluid theory.

We suppose the "electric-fluid" of the one-fluid theory replaced by a crowd of small particles — " electrons," it will be convenient to call them — all exactly similar, and each having exactly the same charge of negative electricity permanently attached to it. According to the best recent determinations, the amount of this charge is 4,l774 x 10-10 electrostatic units, while the mass of each electron is 9'00 x 10-28 grammes. These determinations, which are due to Millikan and Bucherer, are probably accurate to about one part in a thou- sand. To a lower degree of accuracy the radius of the electron is probably about 2 x 10-13 cms. We can form some conception of the intense concentra- tion of mass and electrification in the electron by noticing that a gramme of electrons, crammed together in cubical piling, would occupy only 7 x 10-11 cubic centimetres, while two grammes of electrons placed at a distance of a metre apart would repel one another with a force equal to the weight of 3 x 1022 tons. The electric force of repulsion outweighs the gravitational force of attraction in the ratio of 4*2 x 1042 to one.

A piece of ordinary matter in its unelectrified state contains a certain number of electrons of this kind, and this number is just such that two pieces of matter each in this state exert no electrical forces on one another —

27. 28] Modem View of Electricity 21

this condition in fact defines the unelectrified state. A piece of matter appears to be charged with negative or positive electricity according as the number of negatively-charged electrons it possesses is in excess or defect of the number it would possess in its unelectrified state.

From this it follows that we cannot go on dividing a charge of electricity indefinitely — a natural limit is imposed by the charge of one electron, just as in chemistry we suppose a natural limit to be imposed on the divisibility of matter by the mass of an atom. The modern view of electricity may then be justly described as an "atomic" view. And of all the experimental evidence which supports this view none is more striking than the circumstance that these "atoms" continually reappear in experiments of the most varied kinds, and that the atomic charge of electricity appears always to be precisely the same.

It also follows that in charging a body with electricity we either add to or subtract from its mass according as we charge it with negative electricity (i.e., add to it a number of electrons), or charge it with positive electricity {i.e., remove from it a number of electrons). Since the mass of an electron is so minute in comparison with the charge it carries, it will readily be seen that the change in its mass is very much too small to be perceptible by any methods of measurement which are at our disposal. Maxwell mentions, as an example of a body possessing an electric charge large compared with its mass, the case of a gramme of gold, which may be beaten into a gold-leaf one square metre in area, and can, in this state, hold a charge of 60,000 electro- static units of negative electricity. The mass of the number of negatively electrified electrons necessary to carry this charge will be found, as the result of a brief calculation from the data already given, to be about 10~13 grammes. The change of weight by electrification is therefore one which it is far beyond the power of the most sensitive balance to detect.

On this view of electricity, the electrons must repel one another, and must be attracted by matter which is devoid of electrons, or in which there is a deficiency of electrons. The electrons move about freely through conductors, but not through insulators. The reactions which, as we have seen, must be supposed to occur at the surface of charged conductors between "matter" and "electricity," can now be interpreted simply as systems of forces between the electrons and the remainder of the matter. Up to a certain extent these forces will restrain the electrons from leaving the conductor, but if the electric forces acting on the electrons exceed a certain limit, they will overcome the forces acting between the electrons and the remainder of the conductor, and an electric discharge takes place from the surface of the conductor.

Thus an essential feature of the modern view of electricity is that it regards the flow of electricity as a material flow of charged electrons. Good conductors and good insulators are now seen to mean simply substances in which the electrons move with extreme ease and extreme difficulty respectively.

22 Electrostatics — Physical Principles [ch. i

The law that equal quantities of positive and negative electricity are generated simultaneously means that electrons may flow about, but cannot be created or annihilated.

The modern view enables us also to give a simple physical interpretation to the phenomenon of induction. A positive charge placed near a conductor will attract the electrons in the conductor, and these will flow through the conductor towards the charge until electrical equilibrium is established. There will be then an excess of negative electrons in the regions near the posit -ve charge, and this excess will appear as an induced negative charge. The deficiency of electrons in the more remote parts of the conductor will appear as an induced positive charge. If the inducing charge is negative, the flow of electrons will be in the opposite direction, so that the signs of the induced charges will be reversed. In an insulator, no flow of electrons can take place, so that the phenomenon of electrification by induction does not occur.

On this view of electricity, negative electricity is essentially different in its nature from positive electricity: the difference is something more funda- mental than a mere difference of sign. Experimental proof of this difference is not wanting, e.g., a sharply pointed conductor can hold a greater charge of positive than of negative electricity before reaching the limit at which a discharge begins to take place from its surface. But until we come to those parts of electric theory in which the flow of electricity has to be definitely regarded as a flow of electrons, this essential difference between positive and negative electricity will not appear, and the difference between the two will be adequately represented by a difference of sign.

In the last chapter of the book, it will be explained how recent experi- mental work has traced this essential difference between positive and negative electricity down to its source. We shall see that the positive electricity occurs only in the central cores or " nuclei " of the atom of which matter is constituted, while the outer regions of these atoms consist of negatively- charged particles, the " electrons " already described. For this reason the negative electricity can run about from one atom to another, and even from one conductor to another, but the positive electricity necessarily remains per- manently associated with the same atoms of matter.

Summary.

29. It will be useful to conclude the chapter by a summary of the results which are arrived at by experiment, independently of all hypotheses as to the nature of electricity.

These have been stated by Maxwell in the form of laws, as follows:

Law I. The total electrification of a body, or system of bodies, remains always the same, except in so far as it receives electrification from or gives electrification to other bodies.

28, 29] Maxwells Laws 23