Electromagnetic Waves

ELECTROMAGNETIC WAVES About 1855 James Clerk Maxwell (1831-1879) began the study of electromagnetic phenomena which resulted in his discovery of the electromagnetic theory of electric waves and light, the theory which is of fundamental importance in practically all branches of modern physics. Maxwell studied Faraday's Experimental Researches, and the writings of Green, Stokes and Kelvin. He adopted Faraday's idea about lines of force in electric and mag netic fields, and, like Faraday and Kelvin, believed that the actions between charges and between magnetic poles are transmitted along the lines of force through the field. He concentrated his attention on the fields excited by charges rather than on the charges themselves, regarding the charges as merely singularities in the field.

Maxwell's Equations.

According to Faraday, the current induced in a wire circuit is proportional to the rate of change of the number of unit tubes of magnetic force passing through the circuit. Also, according to Ohm and Kirchhoff, the current is proportional to the electromotive force acting round the circuit. Maxwell supposed that Faraday's result could be applied to any closed curve in a magnetic field, and not only to closed metallic circuits. He supposed that, if the number of unit magnetic tubes through a closed curve is changing, there will be an electromotive force acting round the curve, so that work must be done to move a charge round the curve against the electromotive force. Since, however, the strength of an electric field is merely the force on a unit charge in it, it follows that a varying magnetic field induces an electric field, the lines of force of which form closed curves surrounding the lines of the varying magnetic field. Thus Max well was led to his first fundamental equation of the electromag netic field, which is, in vector notation (see VECTOR ANALYSIS) : where F is the electric, H the magnetic field strength, and it the magnetic permeability of the medium. The meaning of these equations is that the work, required to take a unit charge once round a small plane closed curve against the electric field F, is equal to the rate of diminution of the number of unit tubes of magnetic force passing through the curve.

Maxwell's second fundamental relation was derived from the

theory of the magnetic field of currents. The work required to take a unit magnetic pole once round a current, against the mag netic field of the current, is equal to 47r times the current. This gives curl H = 47ri, where i is the current density. Maxwell did not suppose that the only sort of current is a current in a metallic conductor. Faraday's ideas and experiments on insulators lead him to suppose that, when the electric field in an insulator is changing, there is a current in the insulator. For example, when a condenser, consisting of two parallel metal plates with any insulator between them, is being charged, there is a current flowing into one plate which becomes positively charged, and out of the other plate which becomes negatively charged. Maxwell supposed that the current flows in the insulator as well as in the wires leading to the plates. Each unit tube of electric force, which goes from one plate to the other, starts on a charge 1/4ir and ends on a charge — I/47r, thus the current through the insulator, which Maxwell called a displacement current, is equal to the rate of increase of the number of unit tubes divided by 47r. Along a unit tube of section a, KFa = I so that the current density in the insulator is equal to KF/4ir. In any medium the total current density is then the sum of the conduction current and the displacement current or cF+KF/47r, where a is the conductivity. The equa tion curl H= 4iri therefore becomes curl H = 47r so that, for an insulator in which a = o, we have These equations show that an electromagnetic disturbance, or wave, travels through the medium with velocity equal to i/ µK. Maxwell showed that 1/ A µK, for air, in cms. per sec., is equal to the ratio of the electromagnetic unit of charge to the electro static unit, which was known to be about 3X and so is equal to the velocity of light in air in centimetres per second. It there fore appeared that the velocity of electric waves in air should be equal to the velocity of light in air. Maxwell therefore suggested that light consists of electric waves of short wave length.

The velocity in any insulator is 1/ KK so that, since µ is prac tically the same in all insulators, it follows that the velocity should vary inversely as for different insulators. Taking K= for air, it follows that the refractive index, v, of any in sulator should be given by v = VT. It has been found that this is the case, provided v and K are both measured with electrical oscillations of the same frequency. Maxwell also applied his theory to metallic conductors and crystalline insulators and showed that it leads to results in agreement with the facts.

Kelvin and Maxwell both endeavoured to devise dynamical models of the electromagnetic field, or of the medium usually called the aether, of which the field was supposed to be a modi fication. Indeed, Maxwell's theory of light was first obtained by means of such a dynamical model. The aether was supposed to be an elastic solid, or a fluid filled with vortex filaments or some such dynamical medium. Such models served a useful purpose in aiding the development of the theory, but they have not proved to be of permanent value. It is now generally realized (see SCIENCE ; EN ERGY; ATOM) that the electromagnetic field, with its singularities, the electric charges, is the fundamental entity in terms of which phenomena are to be explained.

In 1873, Maxwell published a great treatise on electricity which contained the results of many new researches. He developed Fara day's ideas on stresses in the electric and magnetic fields and showed that the observed effects can be explained by supposing that there is a tension along the lines of force and an equal pressure at right angles to them. He also worked out a dynamical theory of a system of current circuits taking the magnetic energy to be kinetic and the electrostatic energy to be potential energy. Max well's treatise contained a very valuable account of experimental methods as well as of electrical theories, and it has been the model for later treatises on the subject.

In 1876, H. A. Rowland (1848-1901) showed experimentally that a moving electrostatic charge produces a magnetic field like a current in a conductor. In this celebrated experiment, two paral lel disks forming a condenser were oppositely charged, and one of them was made to rotate about its axis. The field, due to the rotating disk, was measured by means of a suspended magnetic needle which it deflected. Rowland's result has since been con firmed by Rowland and Hutchinson, H. Pender, Eichenwald and E. P. Adams.

The Development of the Electromagnetic Theory.

In 1881, J. J. Thomson worked out the magnetic field due to a mov ing charged sphere. He supposed that the magnetic field was due to the displacement currents in the insulator surrounding the moving sphere. The energy of the magnetic field was proportional to the square of the velocity of the sphere, and J. J. Thomson pointed out that this energy would cause the sphere to have an apparent mass greater than its actual mass. The additional mass due to the energy of the field is now called the electromagnetic mass. J. J. Thomson supposed the velocity of the charged sphere to be small compared with that of light. The electric and magnetic fields when this is not the case were worked out later on Maxwell's theory by Oliver Heaviside and G. F. C. Searle. It was found that, as the velocity approaches that of light, the fields become concen trated near to the plane through the sphere perpendicular to its direction of motion. Horace Lamb, Heaviside and Lord Rayleigh considered the currents induced in conductors by rapidly alter nating fields, and showed that the induced currents are confined to a layer near the surface of the conductor.

In 1883, FitzGerald (1851-1901) showed that, on AIaxwell's theory, a coil carrying a rapidly alternating current should radiate electric waves into the surrounding space, and he suggested that the oscillatory discharge of a Leyden jar might be used to produce a sufficiently rapidly alternating current. Maxwell had shown that electric waves should travel with the velocity of light, but he had not suggested any way of producing such waves. FitzGerald's suggestion was thus of fundamental importance.

In 1884, John Henry Poynting published an important paper on the flow of energy in the electromagnetic field. Consider a tube of force in a magnetic field, and suppose that the strength of the field in the tube is increasing. Then, if we suppose that the energy density in a magnetic field of strength H is where j is the permeability, the energy density in the tube will be increas ing. Energy must therefore be flowing into the tube from outside. When H is increasing, however, there is an electric field round the tube, so that at the surface of the tube we have a magnetic field along the tube and a perpendicular electric field. We therefore conclude that there is a flow of energy in the electromagnetic field, where there is a magnetic field and a perpendicular electric field. and that the direction of the flow is perpendicular to the plane containing the two fields.

Poynting showed that the rate of increase of the electromagnetic energy inside a closed surface could be expressed, by using Max well's equations and Green's theorem, as a surface integral over the closed surface, which he took to represent the inward flow of energy. The elements of the integral were equal per unit area to )FH sin 0 where F and H are the components of the elec tric and magnetic fields along the surface, and 0 is the angle between F and H. The flow of energy, per unit area, per unit time, through the surface, is therefore equal to (1/47r)FH sin O. This result is called Poynting's theorem and it is fundamental in mod ern electromagnetic theory. Poynting showed that, when power is transmitted along a pair of wires, the energy flows in the insulator between the wires, and not in the wires. The energy which gets into the wires is converted into heat and wasted.

Poynting and J. J. Thomson, following Faraday and Maxwell, were inclined to believe in the physical reality of the lines of force in electric and magnetic fields. When the number of unit tubes passing through a circuit increases, they supposed the in crease must be due to tubes moving across the circuit from out side. J. J. Thomson in 1893 published an important treatise entitled Recent Researches in Electricity and Magnetism, in the first chapter of which he discussed electromagnetic theory from the point of view that the electromagnetic field consists of moving tubes of electric force. The magnetic field, he assumed, is a sec ondary effect due to the motion of the electric tubes.

The forces on currents in a magnetic field were explained by supposing that the moving tubes of electric force have momentum which they impart to a conductor when they are absorbed in it. J. J. Thomson showed that the momentum in the field is propor tional to Poynting's flow of energy and in the same direction. This momentum in the field is called the electromagnetic momen tum, and it is of fundamental importance in electromagnetic the ory. Its presence in the field can be proved without assuming the existence of moving tubes of electric force, and the idea of such moving tubes, like the earlier dynamical models of the field, has not proved to be of permanent value.

Hertzian Waves.

About 1886, Heinrich Hertz (1857-1894), a pupil of Helmholtz, began a series of researches which finally established Maxwell's theory of electric waves and light on a solid foundation. FitzGerald had shown theoretically how to produce electric waves, but no way of detecting such waves was known. Hertz discovered that the waves emitted by an electrical oscilla tion of very high frequency could be detected by means of a wire circuit with a very narrow gap in it. The waves induced electrical oscillations in the circuit, and, if the size of the circuit was properly chosen, the induced oscillations were sufficiently powerful to cause sparks to pass across the gap. Hertz's oscillator consisted of two conductors, connected by a straight wire with a spark gap in it. The conductors were charged oppositely, by an induction coil, so that sparks passed across the gap. Sparks were then obtained at the gap of the detecting circuit when it was at considerable dis tances from the oscillator. Hertz supposed that the electric charges oscillated from one side of the oscillator to the other through the sparks, and that these oscillations generated electric waves which were detected by the induced sparks in the detecting circuit. He showed that the waves could be stopped by metallic screens, and that they could be reflected and refracted like light waves. He found that standing waves could be obtained by reflecting a beam of the waves back at normal incidence on a plane reflector. He calculated the frequency of his oscillator, measured the distance between the nodes in the standing waves, so getting the wave length, and found that the product of the wave length and the frequency was equal to the velocity of light. The refrac tive index, for the waves, of a large pitch prism was found to be approximately equal to the square root of the specific inductive capacity of the pitch in accordance with Maxwell's theory.

In Hertz showed that the waves from his oscillators were plane polarized as was to be expected. The electric field in the waves is parallel to the wire joining the two conductors, and the magnetic field is perpendicular to the electric field. Both fields are perpendicular to the direction of propagation. In 1889, Fitz Gerald and Trouton examined the reflection of electric waves at the surface of an insulator and found that when the axis of the oscillator was in the plane of incidence and the angle of incidence had a certain value, then there was no reflection. On then turning the oscillator so that its axis was perpendicular to the plane of incidence, strong reflection was obtained. These results are analo gous to those obtained when plane polarized light is reflected from glass. When the plane of polarization is perpendicular to the plane of incidence, the angle of incidence can be adjusted so that there is no reflection, and on turning the plane of polarization through a right angle there is strong reflection. FitzGerald and Trouton's results therefore show that the electric vibration in light is perpen dicular to the plane of polarization.

Hertz's conclusions have been confirmed by many subsequent researches, and improved methods of generating and detecting electric waves have been developed. By using very small oscilla tors, electric waves only a fraction of a millimeter long have been obtained and studied, and from large oscillators waves many kilo meters long can be obtained easily. The use of electric waves for signalling purposes was initiated in 1896, by Marconi in Italy, and has developed with remarkable rapidity. (See WIRELESS, TELEG RAPHY ; and BROADCASTING : Technical Aspects.) Electrical Effects in Conductors.—In 1879, E. H. Hall of Harvard made an important discovery. He found that, when a conductor carrying a current is placed in a magnetic field, per pendicular to the current, an electromotive force is produced in the conductor, perpendicular to the current and to the magnetic field. This effect, known as the Hall effect, is small, and its direc tion and magnitude depend on the material of the conductor used. If the current density in the metal is i, and the strength of the magnetic field H, then there is a transverse force on the conduc tor equal to Hi per cubic centimetre. This force is presumably due to the force, on the moving electricity in the conductor, which is transferred in some way to the conductor. The transverse forces on moving electricity are in the same direction, for both the positive and negative charges if these move in opposite directions, and the Hall effect is generally believed to be produced in some way by these transverse forces. A satisfactory theory of the Hall effect, however, has not been developed. There is no Hall effect in liquid metals.

Several other related effects have since been discovered. The Ettinghausen effect, discovered in 1887, is a transverse tempera ture gradient, which accompanies the Hall effect in a conductor carrying a current in a transverse magnetic field. In 1856, Kelvin found that the electrical resistance of an iron wire is altered by a magnetic field. This effect has since been found to occur with any metal. The resistance is increased by a small amount proportional to the square of the field strength. The effect is especially large in bismuth. The Nernst effect, discovered in 1886, is a transverse electromotive force, produced in a conductor through which a current of heat is flowing in a transverse magnetic field. The Righi-Leduc effect, discovered in 1887, is the thermal analogue of the Hall effect. A transverse temperature gradient is produced in a conductor, along which heat is flowing, in a transverse mag netic field. The thermal conductivity of metals also is found to be slightly altered by a magnetic field.

In the electromagnetic theory of Maxwell and Hertz, the elec trical properties of material bodies were taken into account by regarding them as continuous media having conductivity, specific inductive capacity and magnetic permeability. The values of these properties differ for different substances, and if they are known for the bodies present in a system, the theory enables the electrical phenomena to be expected in the system to be worked out. The theory has been developed since Hertz's time, by en deavouring to formulate a theory of the nature of material bodies, by means of which their electrical properties can be explained.