Chapter 13b

Helmholtz’s Theory Icon

February 1, 2022

I have dwelt upon the consequences of Ampère’s theory and on his method of explain- ing the action of open currents. It is difficult to disregard the paradoxical and artificial character of the propositions to which we are thus led. We feel bound to think “it cannot be so.”

Helmholtz has been led to look for something else. He rejects the fundamental hypothesis of Ampère— the mutual electro-dynamics.

action of two elements of current reduces to a force along their join. He admits that an clement of current is not acted upon by a single force but by a force and a cou- ple, and this is what gave rise to the celebrated polemic between Bertrand and Helmholtz.

Helmholtz replaces Ampère’s hypothesis:

Two elements of current always admit of an electro-dynamic potential, de- pending solely upon their position and orientation; and the work of the forces that they exercise one on the other is equal to the variation of this potential. Thus Helmholtz can no more do without hypothesis than Ampère, but at least he does not do so without explicitly announcing it. In the case of closed currents, which alone are accessible to experiment, the two theories agree; in all other cases they differ. In the first place, contrary to what Ampère supposed, the force which seems to act on the movable portion of a closed current is not the same as that acting on the movable portion if it were isolated and if it consti- tuted an open current. Let us return to the circuit C 0 , of which we spoke above, and which was formed of a mov- able wire sliding on a fixed wire. In the only experiment that can be made the movable portion αβ is not isolated, but is part of a closed circuit. When it passes from AB to A 0 B 0 , the total electro-dynamic potential varies for twoscience and hypothesis 264 reasons. First, it has a slight increment because the po- tential of A 0 B 0 with respect to the circuit C is not the same as that of AB; secondly, it has a second increment because it must be increased by the potentials of the el- ements AA 0 and B 0 B with respect to C. It is this double increment which represents the work of the force acting upon the portion AB. If, on the contrary, αβ be iso- lated, the potential would only have the first increment, and this first increment alone would measure the work of the force acting on AB. In the second place, there could be no continuous rotation without sliding contact, and in fact, that, as we have seen in the case of closed currents, is an immediate consequence of the existence of an electro-dynamic potential. In Faraday’s experiment, if the magnet is fixed, and if the part of the current external to the magnet runs along a movable wire, that movable wire may undergo continuous rotation. But it does not mean that, if the contacts of the wire with the magnet were suppressed, and an open current were to run along the wire, the wire would still have a movement of contin- uous rotation. I have just said, in fact, that an isolated element is not acted on in the same way as a movable ele- ment making part of a closed circuit. But there is another difference. The action of a solenoid on a closed currentelectro-dynamics. 265 is zero according to experiment and according to the two theories. Its action on an open current would be zero ac- cording to Ampère, and it would not be zero according to Helmholtz. From this follows an important consequence. We have given above three definitions of the magnetic force. The third has no meaning here, since an element of current is no longer acted upon by a single force. Nor has the first any meaning. What, in fact, is a magnetic pole? It is the extremity of an indefinite linear magnet. This magnet may be replaced by an indefinite solenoid. For the definition of magnetic force to have any meaning, the action exercised by an open current on an indefinite solenoid would only depend on the position of the ex- tremity of that solenoid—i.e., that the action of a closed solenoid is zero. Now we have just seen that this is not the case. On the other hand, there is nothing to prevent us from adopting the second definition which is founded on the measurement of the director couple which tends to orientate the magnetic needle; but, if it is adopted, nei- ther the effects of induction nor electro-dynamic effects will depend solely on the distribution of the lines of force in this magnetic field. III. Difficulties raised by these Theories.—Helmholtz’s theory is an advance on that of Ampère; it is necessary,science and hypothesis 266 however, that every difficulty should be removed. In both, the name “magnetic field” has no meaning, or, if we give it one by a more or less artificial convention, the ordinary laws so familiar to electricians no longer apply; and it is thus that the electro-motive force induced in a wire is no longer measured by the number of lines of force met by that wire. And our objections do not proceed only from the fact that it is difficult to give up deeply-rooted habits of language and thought. There is something more. If we do not believe in actions at a distance, electro-dynamic phenomena must be explained by a modification of the medium. And this medium is precisely what we call “magnetic field,” and then the electro-magnetic effects should only depend on that field. All these difficulties arise from the hypothesis of open currents. IV. Maxwell’s Theory.—Such were the difficulties raised by the current theories, when Maxwell with a stroke of the pen caused them to vanish. To his mind, in fact, all currents are closed currents. Maxwell ad- mits that if in a dielectric, the electric field happens to vary, this dielectric becomes the seat of a particular phenomenon acting on the galvanometer like a current and called the current of displacement. If, then, two con-electro-dynamics. 267 ductors bearing positive and negative charges are placed in connection by means of a wire, during the discharge there is an open current of conduction in that wire; but there are produced at the same time in the surrounding dielectric currents of displacement which close this cur- rent of conduction. We know that Maxwell’s theory leads to the explanation of optical phenomena which would be due to extremely rapid electrical oscillations. At that period such a conception was only a daring hypothesis which could be supported by no experiment; but after twenty years Maxwell’s ideas received the confirmation of experiment. Hertz succeeded in producing systems of electric oscillations which reproduce all the properties of light, and only differ by the length of their wave—that is to say, as violet differs from red. In some measure he made a synthesis of light. It might be said that Hertz has not directly proved Maxwell’s fundamental idea of the action of the current of displacement on the galvanometer. That is true in a sense. What he has shown directly is that electro-magnetic induction is not instantaneously propagated, as was supposed, but its speed is the speed of light. Yet, to suppose there is no current of displacement, and that induction is with the speed of light; or, rather, to suppose that the currents ofscience and hypothesis 268 displacement produce inductive effects, and that the in- duction takes place instantaneously—comes to the same thing. This cannot be seen at the first glance, but it is proved by an analysis of which I must not even think of giving even a summary here. V. Rowland’s Experiment.—But, as I have said above, there are two kinds of open conduction currents. There are first the currents of discharge of a condenser, or of any conductor whatever. There are also cases in which the electric charges describe a closed contour, being displaced by conduction in one part of the circuit and by convection in the other part. The question might be regarded as solved for open currents of the first kind; they were closed by currents of displacement. For open currents of the second kind the solution appeared still more simple. It seemed that if the current were closed it could only be by the current of convection itself. For that purpose it was sufficient to admit that a “convection current”—i.e., a charged conductor in motion—could act on the gal- vanometer. But experimental confirmation was lacking. It appeared difficult, in fact, to obtain a sufficient inten- sity even by increasing as much as possible the charge and the velocity of the conductors. Rowland, an extremely skilful experimentalist, was the first to triumph, or toelectro-dynamics. 269 seem to triumph, over these difficulties. A disc received a strong electro-static charge and a very high speed of rotation. An astatic magnetic system placed beside the disc underwent deviations. The experiment was made twice by Rowland, once in Berlin and once at Baltimore. It was afterwards repeated by Himstedt. These physi- cists even believed that they could announce that they had succeeded in making quantitative measurements. For twenty years Rowland’s law was admitted without objec- tion by all physicists, and, indeed, everything seemed to confirm it. The spark certainly does produce a mag- netic effect, and does it not seem extremely likely that the spark discharged is due to particles taken from one of the electrodes and transferred to the other electrode with their charge? Is not the very spectrum of the spark, in which we recognise the lines of the metal of the electrode, a proof of it? The spark would then be a real current of induction. On the other hand, it is also admitted that in an electrolyte the electricity is carried by the ions in mo- tion. The current in an electrolyte would therefore also be a current of convection; but it acts on the magnetic needle. And in the same way for cathode rays; Crookes attributed these rays to very subtle matter charged withscience and hypothesis 270 negative electricity and moving with very high velocity. He looked upon them, in other words, as currents of con- vection. Now, these cathode rays are deviated by the magnet. In virtue of the principle of action and reac- tion, they should in their turn deviate the magnetic nee- dle. It is true that Hertz believed he had proved that the cathodic rays do not carry negative electricity, and that they do not act on the magnetic needle; but Hertz was wrong. First of all, Perrin succeeded in collecting the electricity carried by these rays—electricity of which Hertz denied the existence; the German scientist appears to have been deceived by the effects due to the action of the X-rays, which were not yet discovered. Afterwards, and quite recently, the action of the cathodic rays on the magnetic needle has been brought to light. Thus all these phenomena looked upon as currents of convection, elec- tric sparks, electrolytic currents, cathodic rays, act in the same manner on the galvanometer and in conformity to Rowland’s law. VI. Lorentz’s Theory.—We need not go much further. According to Lorentz’s theory, currents of conduction would themselves be true convection currents. Electricity would remain indissolubly connected with certain mate- rial particles called electrons. The circulation of theseelectro-dynamics. 271 electrons through bodies would produce voltaic currents, and what would distinguish conductors from insulators would be that the one could be traversed by these elec- trons, while the others would check the movement of the electrons. Lorentz’s theory is very attractive. It gives a very simple explanation of certain phenomena, which the earlier theories—even Maxwell’s in its primitive form— could only deal with in an unsatisfactory manner; for example, the aberration of light, the partial impulse of luminous waves, magnetic polarisation, and Zeeman’s ex- periment. A few objections still remained. The phenomena of an electric system seemed to depend on the absolute veloc- ity of translation of the centre of gravity of this system, which is contrary to the idea that we have of the relativ- ity of space. Supported by M. Crémieu, M. Lippman has presented this objection in a very striking form. Imagine two charged conductors with the same velocity of transla- tion. They are relatively at rest. However, each of them being equivalent to a current of convection, they ought to attract one another, and by measuring this attraction we could measure their absolute velocity. “No!” replied the partisans of Lorentz. “What we could measure in that way is not their absolute velocity, but their relativescience and hypothesis

velocity with respect to the ether, so that the principle of relativity is safe.” Whatever there may be in these objec- tions, the edifice of electro-dynamics seemed, at any rate in its broad lines, definitively constructed. Everything was presented under the most satisfactory aspect. The theories of Ampère and Helmholtz, which were made for the open currents that no longer existed, seem to have no more than purely historic interest, and the inextrica- ble complications to which these theories led have been almost forgotten. This quiescence has been recently dis- turbed by the experiments of M. Crémieu, which have contradicted, or at least have seemed to contradict, the results formerly obtained by Rowland. Numerous investi- gators have endeavoured to solve the question, and fresh experiments have been undertaken. What result will they give? I shall take care not to risk a prophecy which might be falsified between the day this book is ready for the press and the day on which it is placed before the public.

THE END

Comments

Avatar
No comments yet. Post a comment in the form at the bottom.

Latest Articles

Moneyless Maharlikan System to Solve Stagflation
Moneyless Maharlikan System to Solve Stagflation
Alternative to General Relativity
Alternative to General Relativity
How to Fix Russia and Ukraine
How to Fix Russia and Ukraine
How to Fix Afghanistan
How to Fix Afghanistan

All Superphysics principles in our books

The Simplified Series