CHAPTER IV
ELECTRIFICATION BY MECHANICAL MEANS
It has been shown in the last chapter that potential may be considered as an attribute of space produced by the presence of a charged conductor. In every point of the space surrounding such a conductor, there acts a force pushing positive electricity one way and negative electricity the opposite way. If the charged body is positively electrified, the potential will be positive all around it, but higher close to the body and lower the farther we recede from it. We must conceive a charge as a something which is adhering to a conducting surface; where there is no conductor there can be no charge, though there may be potential. Now the very definition of a conductor is a body over the surface of which electricity can distribute itself without hindrance, that is to say, only under the influence of the potential force that pushes it. The region of space surrounding the charged in which the potential has a sensible value is called the "electric field." A unit charge brought into any point of this field will experience a force acting in a certain direction; in the case of the field being due to the presence of a charged sphere the force acts either radially outward from or radially inward to the centre of the sphere. Where the conductor is of a more complicated shape, or where it is surrounded by a conducting surface kept at a different potential, for instance, earth potential or zero, there also corresponds to each point of the electric field a particular direction, and obviously one direction only, along which the force acts. A unit positive charge, liberated in any point of the field, will follow the impulse of that force and move from point to point along a particular line, and we may thus speak of a "line of force," meaning thereby the path along which a unit charge, or in fact any charge of positive electricity, is urged.
This conception of lines of force, as characterising the qualities of an electric field, is due to Faraday. Thus far lines of force merely have a geometrical significance, namely, that of the direction of the electric force, but it is easy to see that they must also have a dynamic significance. Obviously if we move along a line of force, the actual magnitude of the mechanical force experienced by the unit charge does not necessarily remain the same. Take the simple case of the field due to a charged sphere hanging free in space. The lines of force are all straight lines converging to the centre of the sphere. If at a distance of one yard our unit charge is repelled with a certain force, then at a distance of half a yard the force would be quadrupled. Thus, although we may travel along one and the same line of force, the magnitude of the force changes inversely as the square of the distance. As we approach the sphere, the potential increases inversely as the first power (not the square) of the distance. Potential and force are two things of different character, namely, energy and mechanical force respectively. We have seen that potential may be considered as an attribute of space, and the idea lies near to also consider electric force as an attribute of space, although as an attribute of a different character. This attribute is a mechanical force, namely, the force exerted on unit positive charge.
Let us see how we could make a mechanical model of the lines of force emanating from a charged sphere. We might represent each line by a straight wire stuck into the surface of the sphere and pointing true to the centre. We should thus get a kind of spherical hedgehog; to represent a strong field due to a large charge we should stick into the sphere more wires, and to represent a weak charge we should use a smaller number of wires, but in all cases the wires would be evenly distributed all over the sphere. An imaginary sphere, laid round the nucleus from which all the wires spring, will be pierced by all the wires whatever may be the radius of this imaginary sphere, but the number of wires piercing a unit of the surface of the imaginary sphere will be inversely proportional to the square of its radius. But we know that the force is also proportional to the inverse square of the distance from the centre. The two things follow the same law, and it is therefore obvious that by a suitable selection of units we may express the force at any point by a number indicating how many wires pierce a unit of the surface of the imaginary sphere laid through the point. Thus the density of the lines of force passing through the surface at the point in question is a measure of the mechanical force exerted on unit charge at that point. This is the dynamic significance of the conception of lines of force introduced by Faraday. The density, or number of lines to the unit surface is called the electric "induction," and the force experienced by unit charge is, then, simply equal to the induction, whilst the mechanical force experienced by a body charged with q units will be q times as great. Writing the symbol B for the induction, the force is given by the formula
B may be considered as of the nature of a flow of force, or "flux," piercing each square centimetre of the imaginary sphere laid through the point in question, and the total flux emanating from the charged nucleus will then be represented by the product of B and the total surface of the imaginary sphere laid round it. It will also in our mechanical model be represented by the total number of wires we have stuck into this nucleus. But the total number is the same whatever be the radius of the imaginary sphere. To get the relation between original charge Q on the nucleus and total flow of force emanating from it, we may therefore choose any radius. By adopting a radius equal to unity we get for the surface the expression 4π, and for the total flux the expression Φ = 4π B. We know that the force on unit pole at unit distance is Q × 112 = Q. We also know that the force is B × 1 = B, from which it follows that B and Q are numerically equal, and hence we find as an expression for the total flux emanating from Q units of electric charge
The conception of lines of force is very useful in forming a mental picture of the properties of an electric field by mechanical analogy, but the analogy must not be taken in too literal a sense. We must not think of lines of force in the same way as we think of the stalks of corn in a field, namely, as physical lines each bound to a definite position. In adopting such a view we would be met at once by the difficulty that our unit charge, being placed midway between two lines of force, would not experience any force. This is contrary to experiment; we cannot find any place in a field of sensible magnitude where the force acting on unit charge is zero. To escape the difficulty some writers use the expression "tube of force" instead of line of force, thereby indicating that the force is not limited to a particular mathematical line, but acts with equal strength in any point of the same transverse section of the tube.
Let us now apply the conception of lines, or tubes of force, to see what must happen if a non-charged conductor is approached to a charged conductor. In Fig. 2 the circle on
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Fig. 2.
the right represents a sphere charged with positive electricity. On the left is a cylinder with rounded ends containing no charge originally. Each tube of force emanating from the charged sphere has the property of pulling negative electricity towards the sphere and pushing positive electricity as far away from it as possible. These forces produce a separation of the two electricities originally combined on the non-charged cylinder, so that the end pointing to the sphere will become negatively and the other end positively electrified. The question is, how strongly? Obviously it is a matter of conflicting forces. The left end of the cylinder contains positive and the right end negative electricity. If the sphere were taken away, the attraction between the two charges would cause them immediately to flow together, and, neutralising each other, the cylinder would again appear uncharged, as it was before we approached it to the sphere. There is thus a separating force due to the sphere, and a uniting force due to the mutual action of the two ends acting simultaneously, and the result is that the quantity of charge which can be accumulated on each end of the cylinder is not unlimited.
Now let us touch the cylinder with the finger. The negative charge has no desire to flow away through our body to earth, for it is attracted by the charge of the sphere, but the positive charge of the cylinder is pushed away by the action of the tubes of force and will flow as far as it can. Before the cylinder was touched it went to the farthest point, namely, the left-hand end of the cylinder, but the moment we touch it we give it a path to flow much farther, namely, through our body to earth, that is, right away to zero potential. We have thus brought the potential of the cylinder to zero, and increased the potential difference between sphere and cylinder. We have strengthened the tubes of force passing from sphere to cylinder. The total flux emanating from the sphere has not altered, for that is strictly limited by the charge originally on the sphere, but whilst with a sphere free in space the flux is evenly distributed all round, we have, by bringing the cylinder near, and especially by discharging its positive electricity to earth, disturbed the symmetrical field of the sphere, making it much denser on its left half, and thus increased the inductive effect on the cylinder. The charge at its left end will be increased. If we now interrupt the connection to earth, we have a negatively charged cylinder, and we may carry this charge to some third conductor, and by touching it with the cylinder impart to it a negative charge. This process may be repeated. Approach the cylinder to the sphere again, discharge the cylinder to earth, then pick it up by its insulating stand and carry it again into contact with the third conductor and so on.
By this process the third conductor becomes negatively charged without the use of a frictional machine or voltaic battery. The third conductor, then, becomes the nucleus of an electric field, and as we know that an electric field cannot be produced without the expenditure of energy, the question arises where that energy comes from. A moment's consideration will show that the energy is given by our hand in carrying the cylinder to and fro. Whilst approaching the uncharged, or weakly negatively charged, cylinder to the sphere we receive energy. There is attraction, because the negative end which is attracted is always nearer than the positive end which is repelled. After the cylinder has been discharged to earth there remains only attraction, and against this attractive force the cylinder has to be pulled away. Here our hand is called upon to impart energy to the system. We electrify the third conductor by the expenditure of energy, that is, by mechanical means. The more often we carry the cylinder to and fro, the more negative electricity do we accumulate on the third conductor, but it is evident that this process cannot go on for ever. We are only able to accumulate a definite charge on the third conductor. As this becomes charged, its tube of force also develops and finally becomes as strong as those of the sphere. Then the third conductor refuses to take any of the negative charge of the cylinder, and the process of accumulation ceases. If we wish it to go on further we must increase the source from which the negative charge of the cylinder is derived, that is, we must charge the sphere more strongly. How are we to increase this positive charge? The most obvious thing is to increase it also by mechanical means, much in the same way as we increase the charge on the third conductor, and this is the principle on which the modern electric machines, the so-called "influence machines," work.
The process is not carried out in the primitive manner here explained merely by way of elucidating a principle, but still the essential feature is retained of a go-between, or carrier of small charges, between the two conductors on which the electricities of opposite sign are to be accumulated. A familiar example of a practical way of making use of this principle is the electrophorus, but I shall not discuss it here, as it may be found in any elementary textbook. I prefer to deal at once with apparatus in which the principle of accumulating action is carried on automatically. It is only apparatus of this kind which has practical importance.
As an example of a very simple kind of automatic apparatus we may take Lord Kelvin's "water-dropping machine." Let,
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Fig. 3.
in Fig. 3, A and B be two metal cylinders supported on insulating stands, and a and b two metal funnels likewise supported. A and a are connected by a wire; B and b are similarly connected. To indicate that the two connecting wires at the crossing point in the drawing do not touch, one is shown as going round it in a little half-circle. This is the usual method used in electrical diagrams of showing that two wires cross without touching. Owing to the metallic connection established by these wires, the potential of A is always the same as the potential of a. Similarly B and b are at the same potential. Into the middle of each cylinder there is carried the discharge nozzle of a water pipe, and the flow of water is regulated by means of a stopcock in such manner that there shall be no continuous stream, but a succession of drops.
The drawing is only diagrammatic, and does not represent the actual shape of the parts. In conductors intended for the accumulation of a charge, all sharp corners must be avoided so as to minimise dispersion of charge, which is strongest the smaller the radius of curvature. Any corner is in reality a curved surface, but with a very small radius of curvature. The different parts of a charge distributed over any surface repel each other. If the surface is quite plane the repelling force between the elementary particles of the charge is parallel to the surface, and there is no component tending to flake electricity off the surface and disperse it into the air. If the surface is curved there is such a component, and it becomes the greater the more sharply the surface is curved. At a sharp corner it becomes very great, and if the corner is drawn out into a sharp point the force is so great that all the charge is dissipated as soon as brought to the conductor. Hence lightning-rods, which are intended to dissipate any charge which may be induced in a building by a charged cloud overhead as quickly as possible, and so avert the threatened stroke, are provided with sharp points. The gilding is not essential, but more in the nature of an extravagant refinement. The only excuse one can find for such a refinement is that gilding protects the iron from rusting, and so preserves the sharpness of the point. In the water-dropping machine we would, of course, also avoid the sharp corners by making the outside of each part more or less spherical, without, however, altering the inner and essential parts.
The connection between Figs. 2 and 3 will be obvious at a glance. The cylinder A corresponds to the charged sphere, and the drop of water hanging from the end of the pipe corresponds to the right-hand end of the cylinder. It becomes negatively electrified by induction, and on falling carries this negative charge to the funnel b. This produces a small increase in the negative charge on the inducing cylinder B. The drops of water falling through B are positively electrified, and on striking the funnel a give up their charge to it, which accession of charge is conveyed to the inducing cylinder A, making it more efficient for charging the drops of water which pass through its interior. We have thus a cumulative action between the inducing cylinders, the drops of water and the collecting funnels. The limit of this cumulative process is reached when the dispersion of charge, due to the growing potential difference, just balances the accession of charge carried by the drops of water from one inducing cylinder to the other. We have here a case of electrification by mechanical means, namely, the motion of drops of water. The energy represented by the electric field between A and B is derived from falling water.
The use of water in an apparatus for producing electrification is not always convenient, and under certain circumstances, as, for instance, on board, ship, quite impossible, because in a sea-way the drops would not fall plumb into the collecting funnels. But it is precisely in submarine telegraphy generally, and also in the process of laying submarine cables, that some apparatus for producing strong electrification is required. This need arises in connection with a receiving instrument known as the syphon recorder. If a permanent record of the telegraphic message is desired, the receiving apparatus itself must write down this message, not in actual letters, but in certain telegraphic code signs on a moving strip of paper. To use a pen in touch with the paper is out of the question, because the mechanical force exerted by the mechanism of the receiving telegraph instrument is, with the feeble electric currents that can be got to pass through a submarine cable, too small to overcome the friction between paper and pen. In order to allow the pen to move unfettered and write freely it must not touch the paper. This is done by using for a pen a capillary glass tube and electrifying the ink. We have then a conductor, namely, the ink, with a fairly sharp point, namely, the capillary end of the tube. It was shown above that the force which causes electricity to flake off from a conductor is very great at a sharp point, and thus the electricity dispersing from the end of the tube takes the ink with it, thus squirting it against the paper. In this manner the slight and unfettered movements of the pen are recorded on the paper without the pen touching it.
The problem, therefore, is to keep the ink electrified notwithstanding that some of the charge is continuously dissipated in the action of squirting the ink on to the paper. It is necessary to replenish the charge, and the apparatus for this purpose, which is also
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Fig. 4.
the invention of Lord Kelvin, is called the "replenisher." The apparatus gives the original charge and replenishes it from time to time. All the telegraph operator has to do is to twist a knob quickly. Fig. 4 is a diagrammatic representation of the essential parts of Lord Kelvin's replenisher. A and B are two segments of a metallic cylinder, insulated from each other and connected respectively to the two conductors g and f, between which a difference of potential is to be established or kept up—in our case ink and paper. Within the cylindrical cavity is another pair of insulated segments a and b, connected by an insulating bridge-piece C mounted on a spindle, by which the inner system may be revolved. The knob above mentioned is fixed to the end of this spindle. By twirling the knob rapid rotation of the two inner segments can be produced, and thus a is alternately brought to face A and B at the same times that b is brought to face B and A respectively. The inner segments have each a projecting piece by which a momentary connection is established with fine wire brushes. These are fixed in the position shown d, e, f, g. The brushes d and e are connected by a wire, and the other two brushes are connected as shown with the outer segments.
To explain the action of the replenisher, let us start with the assumption that A has a small positive and B a small negative charge. It is immaterial how small these charges are, since, as will be seen presently, the action is cumulative, so that the merest trace of a charge quickly grows to a quite formidable value. It may be here mentioned that the same principle is utilised in the well-known electric gas-lighters, where the whole of the mechanism diagrammatically represented in the sketch Fig. 4 is contained in the handle of the instrument. The rotation is produced by pressing a knob, and the cumulative action is vigorous enough to raise the potential of the two outer segments to sparking-point. The spark is produced at the end of a tube, which is held over the issuing gas-jet.
Let us then assume that there is a very feeble charge on A and B. If A is positive, a will receive a very small negative charge and b a very small positive charge. Let the rotation be clockwise. As the inner segments advance, the contact at the brushes is broken, and the negative charge of a is carried towards B. When the inner segment a has made a quarter turn, its contact piece touches the brush f, and thus the feeble charge is given up to B, making its charge just a little stronger than it was at starting. At the same time the feeble charge on b, which is positive, is given up to A, making also that charge a little stronger than it was. After half a turn from the start the segments a and b have changed places. They are again in contact by the brushes d e, and b acquires now a negative and a a positive charge which they carry forward and give up to B and A respectively, again increasing the original charge. Thus at each half revolution of the internal carrier the charges on the outer segments are increased, the process being cumulative, but also in this case limited by the dispersion of electricity, which, with an increasing potential difference, eventually reaches so high a value that the charge brought in each half revolution by the carrier just balances the leakage of electricity during the time it takes to perform the half revolution. The faster we twirl the knob, the shorter is this time, and the smaller the leakage per half revolution. By twirling faster a higher potential between the outer segments can be attained. This means in the electric gas-lighter a more vigorous and effective spark.
When it is required to accumulate large charges and to produce spark discharges of considerable magnitude, machines on a larger scale must be used. These are known under the name of "influence machines." Such machines have been constructed by Toepler, Holtz, Voss and others, but the type most commonly used in England is that designed by Wimshurst, of which Fig. 5 is a diagrammatic representation. Two discs of highly insulating material, such as ebonite or varnished glass, are set co-axially very close together, and supported on horizontal spindles which have opposite direction of rotation. Each disc has pasted on the outside a large number of segments of tinfoil. On each side of the
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Fig. 5.
pair of discs there is fixed a metal bar diametrically across, and provided at its two ends with fine wire brushes just touching the row of sectors as they sweep by when the disc revolves. These two metal bars are set with an inclination of about 45 degrees to the horizontal, but not in the same direction, so that the angle they include is about 90 degrees. The angular setting of the bars may be altered between about 60 and 90 degrees, so as to get the most efficient condition of working. In addition to the two bars with their four brushes, there are the two devices for collecting the electricities of opposite sign. Each consists of a U-shaped rod, the limbs of the U embracing the pair of discs from the outside and being provided with a "comb" of sharp points before which the sectors pass. The collecting combs are set on a horizontal line. The direction of rotation of each disc is such that a particular sector, having just passed a comb, turns through an acute angle in order to reach the brush on the cross bar on the same side.
Fig. 5 is a diagrammatic representation of the Wimshurst machine, but for the sake of greater clearness I have substituted concentric cylinders for the parallel discs. The direction of rotation is shown by the arrows. Let the inner cylinder represent the front disc, and the outer the disc at the back. The discs themselves are not shown, only the segments which are represented by the short lines. The cross bar for the front disc is shown by a straight line, that for the back disc by a curved line. This is done merely to avoid lines crossing each other and thus rendering the diagram less clear. Electrically, a curved conductor is as good as a straight one. The collecting devices are represented by the two pairs of points facing the segments on a horizontal diameter: The conductors in which the charges are accumulated are shown by the circles into which a plus and minus sign is inscribed.
To explain the action of the machine, let us assume that by some means a very slight difference of potential has been imparted to two opposite segments of the outer cylinder, say to the segments A and B. This may be done by approaching a rubbed stick of sealing-wax, but generally such a difference of potential exists naturally. We cannot walk across a dry carpet, or run the hand along a piece of furniture, without producing some slight electrification which has the effect of setting up potential differences between different points of space, and, as the merest trace of such a potential difference suffices to start the cumulative process, machines of the Wimshurst type generally start without the necessity of previous electrical excitation. It suffices to turn the handle and so cause the discs to rotate in the proper sense. Let us then assume that the potential of the segment A is a little higher than that of segment B; in other words, that A has a very slight positive and B an equally slight negative charge. The cross bar with the segments a b is at that moment very much in the same condition as the cylinder in Fig. 2, that is to say, the end pointing to the positive segment A (which takes the place of the sphere in Fig. 2) becomes by induction the place where a negative charge collects, and the end b the place where a positive charge collects, only the induction is augmented because B also influences the induced system in the same sense. As the inner cylinder revolves, a moves to the right and is detached from the brush on the cross bar, and takes its charge with it. The same happens with the segment b, which takes its positive charge to the left. The segments a and b eventually arrive in the positions c and d respectively. In this position they come opposite to two outer segments C and D. The roles are now reversed; it is the charge on the inner segment which produces a displacement of electricity along the cross bars connecting C and D, and the charges on these segments are carried on as the outer cylinder rotates, C moving to the left into the position previously occupied by A, and D moves to the right into the position previously occupied by B. But the charge on C is of the same sign as that with which A started the process, and will therefore act in the same sense, only more strongly, since it has been reinforced by the inductive action just explained. Thus during rotation of the two rows of segments in opposite sense the original very slight electrification is rapidly increased, and a considerable quantity of electricity may be taken off by the action of the collecting combs and accumulated on the electrodes. It will be observed that the segments of both discs, whilst passing each other on the horizontal diameter, are charged with electricity of the same sign, namely, positive on the left and negative on the right.
If we now inquire as to the true cause of electrification, we find that apart from the quite insignificant initial charge on A and B, it is simply the mechanical energy required to produce rotation against the opposing force of electrostatic attraction between the outer and inner segments. A has a positive, and a has a negative charge. These two segments therefore attract each other; as a moves to the right and A to the left, they are pulled apart against this attractive force, and energy is therefore required to produce this motion. It is this energy which, by the action of the machine, is converted into the potential energy represented by the electric field surrounding the two electrodes. To increase the charge it is customary to connect the electrodes with the knobs of two Ley den jars, since by the use of a condenser the quantity of electricity, which can be accumulated with a given difference of potential, is greatly augmented. That energy is used in producing electrification is distinctly felt when working the machine by hand. The machine gets charged after a few turns of the handle, and the operator feels that, as the charging progresses, it gets harder to turn the handle. In large machines the manual work becomes so heavy that it is convenient to use an electric motor for working the machine.