Electromagnetic field

“ Since the medium is a perfect insulator, , the free electricity, is immoveable, and therefore is a function of , and the value of J is either constant or zero, or uniformly increasing or diminishing with the time; so that no disturbance depending on J can be propagated as a wave.
(100) The equations of the electromagnetic field, deduced from purely experimental evidence, show that transversal vibrations only can be propagated. ”

“ The electromagnetic field in ponderable bodies, which to our senses appears in general to vary continuously, would present a different aspect if we were able to discern molecular structure; we should then perceive the individual electrons by which the field is produced, and the rapid fluctuations of electric and magnetie* force between them. As it is, the values furnished by our instruments represent averages taken over volumes which, though they appear small to us, are large compared with molecular dimensions. ”

“ This result cannot be reconciled with the electromagnetic theory of light, unless we suppose that there is less loss of energy when the electromotive forces are reversed with the rapidity of the vibrations of light than when they act for sensible times, as in our experiments.
Absolute Values of the Electromotive and Magnetic Forces called into play in the Propagation of Light.
(108) If the equation of propagation of light is
the electromotive force will be
and the energy per unit of volume will be
where P represents the greatest value of the electromotive force. ”

“ The general equations are next applied to the case of a magnetic disturbance propagated through a non-conductive field, and it is shown that the only disturbances which can be so propagated are those which are transverse to the direction of propagation, and that the velocity of propagation is the velocity v, found from experiments such as those of Weber, which expresses the number of electrostatic units of electricity which are contained in one electromagnetic unit.
This velocity is so nearly that of light, that it seems we have strong reason to conclude that light itself ”

“ A space containing electric currents may be regarded as a field where energy is transformed at certain points into the electric and magnetic kinds by means of batteries, dynamos, thermoelectric actions, and so on, while in other parts of the field this energy is again transformed into heat, work done by electromagnetic forces, or any form of energy yielded by currents. ”

“ To further realize, let the field terminate internally at r=a, giving a cylindrical-surface distribution of electrification, and terminate the tubes of displacement externally upon a coaxial cylindrical surface; we then produce a real electromagnetic plane wave with electrification, and of finite energy. We have supposed the electrification to be carried through the dielectric at speed ν, to keep up with the wave, which would of course break up if the charge were stopped. ”

“ The electrostatic system of measurement is founded on the mechanical action between electrified bodies, and is independent of, and incompatible with, the electromagnetic system; so that the units of the different kinds of quantity have different values according to the system we adopt, and to pass from the one system to the other, a reduction of all the quantities is required.
According to the electrostatic system, the repulsion between two small bodies charged with quantities of electricity is
where is the distance between them. ”

“ All energy is the same as mechanical energy, whether it exists in the form of motion or in that of elasticity, or in any other form. The energy in electromagnetic phenomena is mechanical energy. The only question is, Where does it reside? On the old theories it resides in the electrified bodies, conducting circuits, and magnets, in the form of an unknown quality called potential energy, or the power of producing certain effects at a distance. ”

“ It appears therefore that certain phenomena in electricity and magnetism lead to the same conclusion as those of optics, namely, that there is an ethereal medium pervading all bodies, and modified only in degree by their presence; that the parts of this medium are capable of being set in motion by electric currents and magnets; that this motion is communicated from one part of the medium to another by forces arising from the connections of those parts; that under the action of these forces there is a certain yielding depending on the elasticity of these connections ”

“ It seems then that none of the energy of a current travels along the wire, but that it comes in from the nonconducting medium surrounding the wire, that as soon as it enters it begins to be transformed into heat, the amount crossing successive layers of the wire decreasing till by the time the centre is reached, where there is no magnetic force, and therefore no energy passing, it has all been transformed into heat. ”

“ The energy, by the expenditure of which electrical attractions and repulsions are produced, we suppose to be stored up in the dielectric medium which surrounds the electrified bodies, and not on the surface of those bodies themselves, which on our theory are merely the bounding surfaces of the air or other dielectric in which the true springs of action are to be sought. ”

“ Thus the so-called intensity of an electric current is actually the intensity with which the electricity in question disappears! Electricity serves us in our machines in the same way that food serves a living organism: it gets itself digested, and what matters is the resulting secondary product.
Just as alterations in the electrical condition of space give rise to the appearance of a magnetic field, any alteration of the magnetic state of space gives rise to the appearance of an electrical field. This process is called electromagnetic induction. ”

“ Can a current of electricity in a conductor induce a current in another conductor not in any way connected with the first? Can current electricity produce effects through space? Is there an electromagnetic induction?
It has been seen that a current-carrying wire has a magnetic field, and that magnetic fields can act through space. It is evident, then, that a conductor will be surrounded and cut by lines of force when it is placed in a magnetic field, or near a wire or coil through which a current passes. ”

“ The agreement of the results seems to show that light and magnetism are affections of the same substance, and that light is an electromagnetic disturbance propagated through the field according to electromagnetic laws. ”

“ There, denotes the boundary of the field, which can be determined by other bodies or by an (only imagined) surface; is the inner (scalar) product of vectors and , and the first member of the left-hand side is the "power of the inner forces". The second member contains the normal component of "Poyntings radiation vector".
and gives the radiation sent through the boundary by the electron. Power of the inner forces and radiation appear at the cost of the scalar quantity , which we will call "electromagnetic energy", and which occupies the field with the density ”

“ The most obvious mechanical phenomenon in electrical and magnetical experiments is the mutual action by which bodies in certain states set each other in motion while still at a sensible distance from each other. The first step, therefore, in reducing these phenomena into scientific form, is to ascertain the magnitude and direction of the force acting between the bodies, and when it is found that this force depends in a certain way upon the relative position of the bodies and on their electric or magnetic condition, it seems at first sight natural to explain the facts by assuming the existence of something either at rest or in motion in each body, constituting its electric or magnetic state, and capable of acting at a distance according to mathematical laws. ”

“ If we drive a current from A to D by means of some external E.M.I., say at a junction elsewhere in the circuit, the potential will tend to fall from A to D. But a current in iron from hot to cold cools the metal, that is, the E.M.I. appears to be in opposition to the current, so that the energy moves outwards. The potential, therefore, tends to rise from B to C, and actually will do so if the resistance of BC is negligible compared with that of the rest of the circuit. ”

“ The first term of the right side of (3) may be transformed by substituting for the components of the total current their values in terms of the components of the magnetic intensity, while the second term, the product of the conduction current and the electromotive intensity, by Ohm's law, which states that , becomes , where C is the specific conductivity. But this is the energy appearing as heat in the circuit per unit volume according to Joule's law. ”

“ The energy then which maintains the current, and which works the needle at the further end, travels through the insulating material, the core serving as a means to allow the energy to get in motion.
Again, when the only effect in a circuit is the generation of heat, we have energy moving in upon the wire, there undergoing some sort of transformation, and then moving out again as heat or light. If Maxwell's theory of light be true, it moves out again still as electric and magnetic energy, but with a definite velocity and intermittent in type. ”

“ The Production of Induced Currents in the Secondary Coil.—When the current flows through the [Pg 345] primary it sets up a magnetic field in the core. When the current is interrupted, the field disappears. The increase and decrease in the field of the core induces an E.M.F. in the secondary coil, in accordance with the first law of electromagnetic induction. The E.M.F. produced depends upon (a) the number of turns in the secondary, (b) the strength of the magnetic field and (c) the rate of change of the field. The rate of change in the field is more rapid at the break than at the make. ”

“ If there are two electric currents in the field, the magnetic force at any point is that compounded of the forces due to each current separately, and since the two currents are in connexion with every point of the field, they will be in connexion with each other, so that any increases or diminution of the one will produce a force acting with or contrary to the other. ”

“ The change per second in the sum of the electric and magnetic energies within a surface together with the heat developed by currents is equal to a quantity to which each element of the surface contributes a share depending on the values of the electric and magnetic intensities at the element. ”

“ Gravitation differs from magnetism and electricity in this; that the bodies concerned are all of the same kind, instead of being of opposite signs, like magnetic poles and electrified bodies, and that the force between these bodies is an attraction and not a repulsion, as is the case between like electric and magnetic bodies. ”

“ Now in a conductor, when the field is in a steady state, there is no electromotive intensity, and therefore no motion and no transformation of energy. The energy merely streams round the outside of the conductor, if in motion at all in its neighbourhood. If the field is changing, energy can pass into the conductor, as there may be temporary E.M.I. set up within it, and there will be transformation. But we already know the nature of this transformation, for it constitutes the induced current. ”

“ If we were to go beyond our experimental knowledge and to assign a definite density to a substance which we should call the electric fluid, and select either vitreous or resinous electricity as the representative of that fluid, then we might have normal vibrations propagated with a velocity depending on this density. We have, however, no evidence as to the density of electricity, as we do not even know whether to consider vitreous electricity as a substance or as the absence of a substance. ”

“ The relation between the electromotive force and the amount of electric displacement it produces depends on the nature of the dielectric, the same electromotive force producing generally a greater electric displacement in solid dielectrics, such as glass or sulphur, than in air. ”

“ Maxwell showed how, in general, these forces can be deduced from the values of the electromagnetic energy corresponding to different positions of a system of bodies, or from a consideration of certain stresses which exist in the electromagnetic field and of which he taught us to determine the direction and the intensity. Every student, even of rather elementary physics, now knows that the mutual attraction of two conducting plates between which there is a difference of potential, e.g. ”

“ Several solid bodies in which no such structure as we have supposed can be found, seem to possess a mechanical property of this kind [10] ; and it seems probable that the same substances, if dielectrics, may possess the analogous electrical property, and if magnetic, may have corresponding properties relating to the acquisition, retention, and loss of magnetic polarity. ”

“ Here we have evidence of a force causing an electric current in spite of resistance; electrifying the extremities of a body in opposite ways, a condition which is sustained only by the action of the electromotive force, and which, as soon as that force is removed, tends, with an equal and opposite force, to produce a counter current through the body and to restore the original electrical state of the body ”