Part 11

Coulomb proved that the magnitude of the mutual mechanical force exerted between two charged bodies depends on the amounts of the charges and the distance between them. Faraday called attention to the influence of the medium in which the charges are placed. Thus if two charges of q_1 and q_2 units respectively are placed d centimetres apart in a given medium, the mechanical force f in dynes exerted between them is given by the equation f = (q_1q_2)/(Kd^2), provided the dimensions of the bodies on which the charges are concentrated are small in comparison with d. The coefficient K is called the _dielectric constant_ of the medium, and its value is taken as unity for air.

In accordance with this relationship, _unit charge_ is defined as that charge which repels an equal and similar charge placed at a distance of 1 centimetre in air, with a force of 1 dyne.

If the medium surrounding a charged body be explored with a unit charge, a mechanical force varying in magnitude and direction from point to point will be found to act on the unit charge. In such a case, an _electric field_ is said to exist in the medium.

The _strength of the electric field_ at any point is defined as numerically equal to the mechanical force which would act on a unit charge placed in air (or more strictly in a vacuum) at that point. The _direction_ of the electric field at any point is defined to be the direction of the mechanical force acting on a unit _positive_ charge placed at that point.

It should be noted that the strength of the electric field and the mechanical force are numerically equal only when the dielectric constant of the medium is unity. Thus if F is the field strength, K the dielectric constant, and U the mechanical force acting on a unit charge, F = KU.

It is very convenient to represent an electric field by means of what are called _lines of electric force_. If lines are drawn, starting from a positive charge and ending on a negative charge, such that the tangent to the line at any point is the direction of the electric force at that point, these lines are called lines of electric force. They can be drawn in such a way that the strength of the electric field at any point is numerically equal to the number of lines of electric force passing through unit area surrounding that point (and taken at right angles to the direction of the force). The lines of electric force will thus completely represent the electric field.

Further, if the following properties are attributed to the lines of electric force, viz. (_a_) that a line of electric force tends to shorten itself as far as possible; (_b_) that lines of electric force mutually repel one another; then all the phenomena due to the presence of an electric field may be interpreted by the behaviour of the lines of electric force.

Figs. 1 and 2 show the lines of electric force in the space surrounding two charged spheres. Fig. 1 shows the case where the charges are opposite, fig. 2 the case where they are similar. In fig. 1 the attraction between the spheres may be thought of as due to the tendency of the lines of force to shorten themselves. Similarly, the mutual repulsion of the spheres in fig. 2 may be regarded as a consequence of the mutual repulsion of the lines of force.

The distribution of a charge upon an insulated conductor isolated in space depends upon the shape of the conductor. If the conductor is spherical, the charge is uniformly distributed. If the curvature varies from point to point, the quantity of charge per unit area, or the _electric surface density_, will vary from point to point. The sharper the curvature is, the greater the surface density will be. In fig. 3 the distance of the dotted lines from the surface of the conductors is proportional to the surface density. These lines, therefore, give a graphical representation of the distribution of charge. In sharply pointed conductors nearly the whole charge will be concentrated at the pointed end. Owing to the large charge per unit area at the pointed part, particles of dust, water-vapour, &c., will be powerfully attracted, will become charged by conduction, and will then be powerfully repelled. In this way the original charge will be rapidly dissipated. This effect may be shown by keeping a sharply pointed conductor powerfully charged by an electric machine. The streaming of the particles from the point produces a wind which is sufficient to blow out the flame of a candle.

Conductors which are intended to retain their charge for a long period must be smooth and polished, and the maximum curvature must be as small as possible. In lightning-conductors practical advantage is taken of this 'power of points' to dissipate a charge rapidly.

The distribution of the charge on a conductor is influenced by the presence of other conductors, whether charged or not. This is due to what is called _electrostatic induction_. If an uncharged insulated conductor B is brought near a charged conductor A, a charge of the _opposite_ kind is induced on the parts of B nearer to A, and a charge of the _same_ kind on the parts farther away from A. Since B was originally uncharged, these induced charges are equal in amount.

If B is now removed to a distance, the induced charges neutralize one another, and B returns to its original uncharged state.

While B is near A, let the induced charge of the _same_ kind as the charge on A be neutralized by touching B with an earth-connected conductor, say the finger. On removing B to a distance, it will no longer be uncharged as before, but will have a charge of the _opposite_ kind from that on A. B is now said to have been _charged by induction_.

It is instructive to view these phenomena in the light of the conception of lines of electric force. When B is brought up towards A, some of the lines of force associated with the charge on A, and originally linked to surrounding objects, will now, owing to the tendency of the lines to shorten themselves, be linked to B. At the same time an equal number of lines (of opposite direction relative to B) will link B to the nearest surrounding objects.

Since by definition a line of force starts from a positive charge and ends on a negative charge, the charge on the parts of B nearer to A will be of the _opposite_ kind to that on A, but the charge on the part farther from A will be of the _same_ kind as that on A. When the earth-connected conductor is brought near B, the lines formerly linking B to surrounding objects will link B to the earth-connected conductor. Finally, when the latter touches B, these lines shorten themselves indefinitely and disappear.

The attraction of light particles to a charged body is explained by electrostatic induction. The charge of opposite kind induced on the particle being nearer than that of the same kind, the particle is attracted. When it touches the charged body, the charge of opposite kind is neutralized, and the charge of like kind now left on the particle causes repulsion to take place. If the electrified body is an insulator, the neutralization of the charges only takes place slowly, and consequently it may be some time before the particle is repelled.

If two charged conductors be connected by a wire, in general it will be found that a flow of electricity from one to the other will take place. This flow is said to be due to a _difference of electric potential_ between the two conductors. If no flow takes place, then the difference of potential is zero. Electric potential difference (the contraction P.D. is commonly used) is numerically equal to the work done in carrying a unit charge from the one conductor to the other. If the work is done _against_ the electric forces, in moving a unit positive charge from A to B, then B is said to be at a higher potential than A. Although actually it is with _differences_ of potential that we have always to deal, it is convenient in many cases to refer these differences to a zero, and speak of _the potential_ at a point. The ideal zero of potential would be the potential at a point infinitely far removed from all electrified bodies. In practice it is convenient to regard the potential of the earth as zero. The potential at a point is then numerically equal to the work done in carrying a unit positive charge from earth to the point. The potential at every point on a conductor is obviously the same, for if it were not so, a flow of charge would take place and equalize the potential. If an insulated uncharged conductor be connected by a wire to a charged conductor, a flow of charge will take place until every point on both conductors is at the same potential. The quantity of charge which each conductor will then have depends on what is called the _capacity_ of the conductor.

The _capacity of a conductor_ is defined as the quantity of electricity with which it must be charged in order to raise its potential from zero to unity. Thus if Q be the quantity, V the potential, and C the capacity, we have C = Q/V. The potential of a conductor is, therefore, directly proportional to the charge upon the conductor, and inversely proportional to the capacity of the conductor.

The capacity of a conductor may be increased by placing close to it another conductor which is kept at zero potential. Such an arrangement is called a condenser. The Leyden jar (see _Leyden Jar_) is a well-known example of a condenser. The capacity depends not merely on the dimensions of the conductors and the distance between them, but also upon the nature of the dielectric separating them. The ratio of the capacity of a condenser with a given dielectric to the capacity it would have with an air dielectric, is called the _specific inductive capacity_ of the dielectric. Numerically the specific inductive capacity of a dielectric is equal to the dielectric constant already mentioned.

In the experimental investigation of electrostatic phenomena it is convenient to have appliances which will supply charges as they are required. The simplest appliance of this kind is the electrophorus, which consists of a disc of ebonite or other suitable material with a metallic base, and a metal disc of slightly smaller diameter having an insulating handle attached at right angles to its surface (see fig. 5). To use the electrophorus, the ebonite is given a negative charge by striking it with fur or flannel. The metal disc is then placed on top of the ebonite plate. Since the ebonite is an insulator, no general neutralization of the positive induced charge on the lower side of the metal disc can take place. The negative charge on the upper surface of the metal disc is then neutralized by touching with the finger. The disc is thus left positively charged. The disc is then lifted by the insulating handle, and the charge utilized as required. Theoretically speaking, this process may be repeated continuously without affecting the original charge on the ebonite plate, but in practice the ebonite has to be re-excited from time to time on account of the loss of charge by leakage. More elaborate appliances of many different forms have been used, but the only one of these _electric machines_, as they are called, which is now commonly employed is the _Wimshurst machine_. This machine consists of two circular plates of glass or ebonite carrying equal even numbers of tinfoil sectors symmetrically placed on their outer surfaces. A pair of brass arms carrying wire brushes, which simultaneously make contact with diametrically opposite sectors on each plate, is so arranged as to lie at an angle of about 45deg to the horizontal, and to be at right angles to one another. A pair of combs is placed at each end of the horizontal diameter of the plates, so that the sectors pass close to the teeth of these combs. The combs serve as collectors, and are connected one pair to the positive pole, and the other pair to the negative pole of the machine. The general appearance of the machine is shown in fig. 6. The machine acts on the induction principle, and if kept warm and dry is self-exciting.

The _electroscope_ is a simple piece of apparatus for detecting the presence of an electric charge, determining its sign (positive or negative), and making a very rough comparative estimate of its potential. It consists of a pair of strips of gold-leaf attached to a brass rod terminating in a brass cap. The whole is enclosed in a glass case, or a case having glass sides. The base is made of conducting material. The sides of the case are coated internally with tinfoil (or two rods connected to the base project upwards to the level of the gold-leaf strips). The general appearance of one form of electroscope is shown in fig. 7. The gold-leaf strips, the brass rod, and the cap must be carefully insulated. When a charged body is brought near the electroscope the leaves become charged similarly by induction. The repulsion due to the similar charges causes the leaves to diverge.

If the cap be touched with the finger, the charge on the leaves is neutralized, and the leaves collapse. On removing the charged body the leaves diverge again, owing to the spreading of the charge on the cap, which was held by the inducing charge, over the whole conductor, including the leaves. The electroscope is thus charged by induction. It may also be charged by conduction, i.e. by the direct transfer of a charge to the electroscope. When we know the kind of charge, positive or negative, which has been given to the electroscope, an unknown charge can be tested. If the approach of the unknown charge causes a further divergence of the leaves, then it is of the same kind as that with which the electroscope is charged.

When accurate quantitative measurements have to be made, an instrument called an _electrometer_ is used. This instrument, the development of which is due chiefly to Lord Kelvin, is capable of making accurate measurements of electrostatic potential differences down to quite low values.

Essentially an electrometer consists of a light suspended conductor which moves within four fixed quadrants. Opposite pairs of these quadrants are connected together, one pair to one terminal, and the other pair to the other terminal of the instrument. The P.D. to be measured is applied at these terminals. The suspended conductor or 'needle' is charged to a definite high potential, and the deflection produced is observed from the movement of a spot of light reflected from a mirror attached to the suspending fibre. In this case the deflection is proportional to the P.D. between the quadrants. For measuring a high P.D., the needle may be connected to one pair of quadrants. With such an arrangement the instrument is less sensitive, and the deflection is proportional to the square of the P.D. between the quadrants.

_Current Electricity._ The phenomena connected with the flow of electricity through a conductor come under this heading. Such a flow of electricity will take place if by some means the ends of the conductor are maintained at different potentials. An _electric current_ is then said to exist in the conductor. The difference of potential may be maintained by chemical action (see _Daniell's Cell_; _Electric Battery_), by electro-dynamic action (see _Generator_), or by heat action (see _Thermo-electricity_). The magnitude of the current which will flow when a steady P.D. is maintained between the ends of the conductor is determined by what is called the electrical _resistance_ of the conductor. The resistance R is defined as the ratio of the applied potential difference V to the current I produced, i.e. R = V/I. This is a partial expression of Ohm's Law for the Electric Circuit, which in its most general form states that the current which flows at any instant in an electric circuit is equal to the algebraic sum of the electromotive forces existing in the circuit at that instant, divided by the total resistance in the circuit at that instant (see _Electromotive Force_).

For the particular case where the algebraic sum E of the electromotive forces is steady, and the total resistance R is not varying, we have I = E/R. This is the form which applies to steady direct currents. If the current is changing (whether alternating or merely varying in value), varying E.M.F.'s, in addition to the applied E.M.F., exist in the circuit, and the above expression no longer holds good.

The resistance of a conductor depends on its material, and varies directly as the length, and inversely as the cross-section of the conductor. Thus R = [rho](l/A), where [rho] is the specific resistance of the material, l the length of the conductor, and A the cross-sectional area of the conductor. The _specific resistance_ is the resistance between opposite faces of a unit cube of the material at a definite temperature (usually 0deg C.). The resistance of a conductor varies to a greater or less extent with variation of temperature.

For pure metals the resistance increases considerably with increase of temperature. With certain alloys the change is so slight as to be negligible. In some alloys, and in carbon and insulating materials, the resistance falls with increase of temperature.

_Measurement of Resistance._--Low resistances can most conveniently be measured by a fall of potential method, based on the relationship R = V/I. The current may be read by an ammeter, and the potential difference by a low-reading voltmeter (see _Electrical Measuring Instruments_). Where greater accuracy is required, a constant current is sent through the resistance to be measured, and also through a known standard resistance of about the same value. A sensitive galvanometer (see _Galvanometer_) is used to compare the P.D. across the unknown resistance with that across the standard. Since the current is the same through both, the resistances will be proportional to the galvanometer deflections, and from the known value of the standard resistance the value of the unknown resistance can be calculated. Resistances of moderate value are best measured by a Wheatstone Bridge, or one of its modifications (see _Wheatstone Bridge_).

A substitution method is more suitable for high resistances. A galvanometer is connected in series with a standard high resistance and a steady source of E.M.F. The deflection is noted. The unknown resistance is now substituted for the standard, and the new deflection noted. Provided the resistance of the galvanometer and other parts of the circuit is negligible in comparison with the resistance to be measured, the resistances are inversely as the deflections. The unknown resistance is, therefore, equal to the ratio of the first to the second deflection multiplied by the value of the standard resistance. For insulation tests on installations, direct-reading instruments are frequently used (see _Ohmmeter_).

_Effects of an Electric Current._--When a current flows in a conductor, the temperature of the conductor is raised. This is due to the power dissipated on account of the resistance of the conductor. The power dissipated is equal to I^2R watts, and by giving suitable values to I and R any required amount of heat per second can be obtained. This _heating effect_ of the current is made use of in electric lighting, electric heating and cooking, in electric furnaces, and in certain electro-medical appliances.

If a magnetic needle is brought near a conductor carrying a current, it will be found to be deflected. This is due to the magnetic field, which is always associated with an electric current. This _electro-magnetic effect_ is of the utmost practical importance (see _Electro-magnetism_; _Generator_; _Electric Motors_).

When a current is passed through a conducting liquid, such as a solution of a metallic salt or a salt in a fused state, chemical action takes place. The behaviour of such a conductor is entirely different from that of a metallic conductor, since a current can flow in it only if chemical dissociation takes place (see _Electrolysis_).

Practical use of electrolysis is made in electroplating, the production of electrotype blocks for printing, the refining of copper, and the production of metallic sodium and potassium. Electrolysis is also used as a means of storing electrical energy in a chemical form (see _Secondary Cell_).

An electric current may be constant in direction (_direct current_), or may alternate in direction with a certain frequency (_alternating current_). Alternating currents have advantages for the transmission of large amounts of power over considerable distances (see _Electric Power Transmission and Distribution_), and may be used for electric lighting and the operation of electro-dynamic machines and apparatus (see _Electric Motors_).

BIBLIOGRAPHY: B. Kolbe, _Introduction to Electricity_; S. P. Thompson, _Elementary Lessons in Electricity_; Starling, _Electricity and Magnetism_; Poynting and Thomson, _Electricity_; W. E. Ayrton, _Practical Electricity_; C. R. Gibson, _Electricity of To-day_; Clerk-Maxwell, _Electricity and Magnetism_; E. E. Brooks and A. W. Poyser, _Magnetism and Electricity_.

ELECTRIC LIGHT, a light obtained by the conversion of electric energy into light energy. The usual method is to heat some material to incandescence by passing an electric current through it. The material may be carbon (arc lamps), tungsten wire (all modern incandescent lamps), mercury vapour (mercury vapour lamps), or volatilized metallic salts (flame arc lamps). Other materials have been used, such as zirconium, yttrium, and thorium oxides, and osmium and tantalum among the metals, but they have been displaced entirely by the materials mentioned above.

Ordinary arc lamps, and even flame arc lamps, are being displaced by the modern high-candle-power gas-filled tungsten lamp. Flame arc lamps have a high efficiency, and are still largely used for street lighting, but the cost of the frequent trimming required, even in lamps of the magazine type, gives the gas-filled lamp an advantage over them. Lamps of the mercury vapour class have a high efficiency, and the light has a high actinic value which is valuable for certain photographic processes, but the absence of the red and orange part of the spectrum gives the light a characteristically ghastly effect which limits the use of this type of lamp.

_The Carbon Arc._--Although the arc lamp has fallen into disuse, the carbon arc is still extensively employed for projection work, as in cinema projectors and in searchlights. The action of the carbon arc is as follows: If a potential difference of about 50 volts is maintained between a pair of carbon rods, and the tips of the rods are momentarily brought into contact and then separated by a short distance, then the current is maintained by an arc across the gap. The temperature of the positive tip rises to about 4000deg C., and the tip itself soon becomes hollowed, forming what is called the _positive crater_.

The illustration below represents the two carbons of the arc light as they appear when cold, the positive carbon being marked + and the negative -. The central figure is a magnified representation such as can be obtained by throwing an image of the burning carbons on a screen by means of a lens. In fig. 1 the upper rod is the positive one, and the hollowed shape of the tip is clearly shown. The negative tip becomes roughly pointed in shape, and its temperature is about half that of the positive crater.