19. FIELDS OF FORCE 89. When an electric current flows through a conductor, power is consumed and heat produced inside of the conductor. In the space outside and surrounding the conductor, a change has taken place also, and this space is not neutral and inert any more, but if we try to move a solid mass of metal rapidly through it, the motion is resisted, and heat produced in the metal by induced currents. Materials of high permeability, as iron filings, brought into this space arrange themselves in chains; a magnetic needle is moved and places itself in a definite direction. Due to the passage of the current in the conductor, there are therefore in the spaces outside of the con- ductor — where the current does not flow — forces exerted, and FIELDS OF FORCE 113 this space then is not neutral space, but has become a field of force, and the cause of the field, in this case the electric current in the conductor, is its "motive force." As in this case the actions exerted in the field of force are magnetic, the space surrounding a conductor traversed by a current is a field of magnetic force, and the current in the conductor is the magneto- motive force. In the space surrounding a ponderable mass, as our earth, forces are exerted on other masses — which cause the stone to fall toward the earth, and water to run down hill — and this space thus is a field of gravitational force, the earth the gram- motive force. In the space surrounding conductors having a high potential difference, we observe a field of dielectric force, that is, electro- static or dielectric forces are exerted, and the potential difference between the conductors is the electromotive force of the dielectric field. The force exerted by the earth as gravimotive force, on any mass in the gravitational field of the earth, causes the mass to move with increasing rapidity. The direction of motion then shows the direction in which the force acts, that is, the direc- tion of the gravitational field. The force g, which the field exerts on unit mass, that is, the acceleration of the mass, measures the intensity of the field: in the gravitational field of the earth 981 cm g sec. The force acting upon a mass m, then, is:F = gm, and is called the weight of the mass. In the same manner, in the magnetic field of a current as magnetomotive force, the intensity H of the magnetic field is measured by the force F which the field exerts on a magnetic mass or pole strength m: F = Hm; the intensity K of the di- electric field of a potential difference as electromotive force is measured by the force F exerted upon an electric pole strength e: F = Ke', the direction of the force represents the direction of the field of force. 90. This conception of the field of force is one of the most important and fundamental ones of all sciences and applied sciences: a condition of space, brought about by some exciting cause or motive force, whereby the space is not neutral any more, but capable of exerting forces on anything susceptible to these forces: mechanical forces on masses in a gravitational field, magnetic forces on magnetic materials in a magnetic field, 114 ELEMENTS OF ELECTRICAL ENGINEERING A. — A photograph of a mica-filing map of the dielectric lines of force- between two cylinders. B. — A photograph of an iron-filing map of the magnetic lines of force about. two cylinders. C. — A photographic superposition of A and B representing the magnetic- and dielectric fields of the space surrounding two conductors which are; carrying energy. FIG. 45. FIELDS OF FORCE 115 dielectric forces on dielectrics in a dielectric field, etc. The field of force then is characterized by having, at any point, a definite direction — the direction in which the force acts — and a definite intensity, to which the forces are proportional. Such fields of force can be graphically represented by lines showing the direction in which the force acts: the lines of force and, at right angles thereto, the equipotential lines or surfaces, as the direction in which no force acts. Thus the lines of gravita- tional force of the earth are the verticals, the equipotential sur- faces, or level surfaces, are the horizontals. Such pictures of a field of force also illustrate the intensity: where the lines of force and therefore the equipotential lines come closer together, the field is more intense, that is, the forces greater. FIG. 46. — A mathematical plot of fields shown in C. Magnetic fields may be demonstrated by iron filings brought into the field; dielectric fields by particles of a material of high specific capacity, such as mica. Fig. 45 shows the dielectric field of a pair of parallel conductors, the magnetic field between these conductors, and their combination. Fig. 46 shows the same as calculated. As further illustration, Fig. 47 shows, from observation, half of the dielectric field between a rod with circular disc, as one terminal, passing symmetrically through the center of a cylinder placed in a circular hole in a plate as other terminal: the lines of force pass from terminal to terminal; the equipotential surfaces intersect at right angles (A 10,292). 91. In electrical engineering we have to deal with the electrical quantities: voltage, current, resistance, etc.; the magnetic quan- 116 ELEMENTS OF ELECTRICAL ENGINEERING titles: magnetic flux, field intensity, permeability, etc.; and the di- electric quantities: dielectric flux, field intensity, permittivity, etc. The electric current is the magnetomotive force F which produces the magnetic field, acting upon space. It is expressed in amperes, or rather in ampere-turns, and thus is an electrical quantity, its Rod V-0 Plane Hole FIG. 47. — Observed dielectric field. unit being determined by the unit of current, as the ampere-turn equal to 10"1 absolute units. The magnetomotive force per unit length of the magnetic circuit then is the magnetizing force or magnetic gradient f, in ampere-turns per centimeter, hence still an electrical quantity. Proportional thereto, and of the same dimension, is the FIELDS OF FORCE 117 magnetic field intensity H. It differs from the magnetic gradient merely by a numerical factor 4 TT; H = 4?r/ 10"1. Magnetic field intensity is a magnetic quantity, and its unit defined by the magnetic forces exerted in the field, thus different from the unit of magnetic gradient, which is determined by the unit of electric current; hence the factor 4 IT. The factor 10"1 merely reduces from amperes to absolute unit. If then v is the magnetic conductivity of the material in the magnetic field, called its permeability, B = pH is the magnetic flux density, and the total magnetic flux <1> is given by the density B times the area or section of the flux. Or, passing directly from the magnetomotive force F to the F magnetic flux, by the conception of the magnetic circuit: 3> = „> where R is the magnetic resistance, or reluctance of the magnetic circuit. R is an electric quantity, and does not contain the 4 TT. In the dielectric field, the potential difference e is the electro- motive force expressed in volts. The electromotive force per unit length of the dielectric circuit is the electrifying force or voltage gradient or dielectric gradient g, expressed in volts per centimeter. This is still an electric quantity. Proportional thereto by a numerical factor is the dielectric quantity: dielectric field intensity K = . 2, and if k is the dielectric conductivity of the medium in the dielectric field, called specific capacity or permittivity, the dielectric flux density is D = kK, and the total dielectric flux ^ is flux density times area. Here again, at the transition from the electric quantity "gradient" to the dielectric quantity " field intensity," a numer- ical factor 4 irv2 enters, the one quantity being based on the volt as unit, the other on unit force action, v is the velocity of light, 3 X 1010, and the factor v2 the result of the convention of assum- ing the permittivity of empty space as unity. It is now easy to remember, where in the electromagnetic system of units the factor 4-Tr enters: it is at the transition from the electrical quantities to the magnetic or dielectric quantities, from gradient to field intensity. 92. The dielectric field and the magnetic field are analogous, and to magnetic flux, magnetic field intensity, permeability, as used in dealing with magnetic circuits, correspond the terms 118 ELEMENTS OF ELECTRICAL ENGINEERING dielectric flux, dielectric field intensity, permittivity, as used in dealing with the electrostatic fields of high potential apparatus, as transmission insulators, transformer bushings, etc. The fore- most difference is that in the magnetic field, a line of force must always return into itself in a closed circuit, while in the electro- static or dielectric field, a line of force may terminate in a con- ductor. The terminals of the lines of electrostatic flux, ^ at the conductor, then are represented by the conception of a quantity of electricity or electric charge, Q, being located on the con- ductor. Thus, at the terminal of the line of unit dielectric flux, unit electric quantity is located on the conductor. Dielectric flux ^ and electric quantity or charge Q thus are identical, and merely different conceptions of the dielectric circuit : Q = *. In using the conception of electric quantity Q, we consider only the terminals of the lines of dielectric flux, that is, deal merely with the effect of the dielectric flux on the electric circuit which produced it. This conception is in many cases more convenient, but it necessarily fails, when the distribution of the dielectric flux in the dielectric field is of importance, such as is the case when dealing with high dielectric field intensities, approach- ing the possibility of disruptive effects in the field of force, or when dealing with the effect produced by the introduction of ma- terials of different permittivity into the dielectric field. There- fore, with the increasing importance of the dielectric field in engineering, the conception of electric quantity, or charge, is gradually being replaced by the conception of the dielectric flux and the dielectric field, analogous to the magnetic field, which has replaced the previous conception of " magnetic poles."