Notes on Recent Researches in Electricity and Magnetism ppt

The Project Gutenberg EBook of Notes on Recent Researches in Electricity and Magnetism, by J. J. Thomson This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.net Title: Notes on Recent Researches in Electricity and Magnetism Intended as a Sequel to Professor Clerk-Maxwell\’s Treatise on Electricity and Magnetism Author: J. J. Thomson Release Date: June 27, 2011 [EBook #36525] Language: English Character set encoding: ISO-8859-1 *** START OF THIS PROJECT GUTENBERG EBOOK RECENT RESEARCHES ELECTRICITY, MAGNETISM *** NOTES ON RECENT RESEARCHES IN ELECTRICITY AND MAGNETISM INTENDED AS A SEQUEL TO PROFESSOR CLERK-MAXWELL’S TREATISE ON ELECTRICITY AND MAGNETISM BY J. J. THOMSON, M.A., F.R.S. Hon. Sc.D. Dublin FELLOW OF TRINITY COLLEGE PROFESSOR OF EXPERIMENTAL PHYSICS IN THE UNIVERSITY OF CAMBRIDGE Oxford AT THE CLARENDON PRESS 1893 Oxford PRINTED AT THE CLARENDON PRESS BY HORACE HART, PRINTER TO THE UNIVERSITY Produced by Robert Cicconetti, Nigel Blower and the Online Distributed Proofreading Team at http://www.pgdp.net (This file was produced from images generously made available by Cornell University Digital Collections) Transcriber’s Notes A small number of minor typographical errors and inconsistencies have been corrected. See the DPtypo command in the L A T E X source for more information. PREFACE In the twenty years which have elapsed since the first appearance of Maxwell’s Treatise on Electricity and Magnetism great progress has been made in these sciences. This progress has been largely—perhaps it would not be too much to say mainly—due to the influence of the views set forth in that Treatise, to the value of which it offers convincing testimony. In the following work I have endeavoured to give an account of some re- cent electrical researches, experimental as well as theoretical, in the hope that it may assist students to gain some acquaintance with the recent progress of Electricity and yet retain Maxwell’s Treatise as the source from which they learn the great principles of the science. I have adopted ex- clusively Maxwell’s theory, and have not attempted to discuss the conse- quences which would follow from any other view of electrical action. I have assumed throughout the equations of the Electromagnetic Field given by Maxwell in the ninth chapter of the second volume of his Treatise. The first chapter of this work contains an account of a method of re- garding the Electric Field, which is geometrical and physical rather than analytical. I have been induced to dwell on this because I have found that students, especially those who commence the subject after a long course of mathematical studies, have a great tendency to regard the whole of Maxwell’s theory as a matter of the solution of certain differential equa- tions, and to dispense with any attempt to form for themselves a mental picture of the physical processes which accompany the phenomena they are investigating. I think that this state of things is to be regretted, since it retards the progress of the science of Electricity and diminishes the value of the mental training afforded by the study of that science. In the first place, though no instrument of research is more powerful than Mathematical Analysis, which indeed is indispensable in many de- partments of Electricity, yet analysis works to the best advantage when PREFACE v employed in developing the suggestions afforded by other and more physi- cal methods. One example of such a method, and one which is very closely connected with the initiation and development of Maxwell’s Theory, is that of the ‘tubes of force’ used by Faraday. Faraday interpreted all the laws of Electrostatics in terms of his tubes, which served him in place of the symbols of the mathematician, while in his hands the laws according to which these tubes acted on each other served instead of the differential equations satisfied by such symbols. The method of the tubes is distinctly physical, that of the symbols and differential equations is analytical. The physical method has all the advantages in vividness which arise from the use of concrete quantities instead of abstract symbols to represent the state of the electric field; it is more easily wielded, and is thus more suitable for obtaining rapidly the main features of any problem; when, however, the problem has to be worked out in all its details, the analytical method is necessary. In a research in any of the various fields of electricity we shall be acting in accordance with Bacon’s dictum that the best results are obtained when a research begins with Physics and ends with Mathematics, if we use the physical theory to, so to speak, make a general survey of the country, and when this has been done use the analytical method to lay down firm roads along the line indicated by the survey. The use of a physical theory will help to correct the tendency—which I think all who have had occasion to examine in Mathematical Physics will admit is by no means uncommon—to look on analytical processes as the modern equivalents of the Philosopher’s Machine in the Grand Academy of Lagado, and to regard as the normal process of investigation in this subject the manipulation of a large number of symbols in the hope that every now and then some valuable result may happen to drop out. Then, again, I think that supplementing the mathematical theory by one of a more physical character makes the study of electricity more valu- able as a mental training for the student. Analysis is undoubtedly the greatest thought-saving machine ever invented, but I confess I do not think it necessary or desirable to use artificial means to prevent students from thinking too much. It frequently happens that more thought is required, and a more vivid idea of the essentials of a problem gained, by a rough solution by a general method, than by a complete solution arrived at by the most recent improvements in the higher analysis. PREFACE vi The method of illustrating the properties of the electric field which I have given in Chapter I has been devised so as to lead directly to the dis- tinctive feature in Maxwell’s Theory, that changes in the polarization in a dielectric produce magnetic effects analogous to those produced by con- duction currents. Other methods of viewing the processes in the Electric Field, which would be in accordance with Maxwell’s Theory, could, I have no doubt, be devised; the question as to which particular method the stu- dent should adopt is however for many purposes of secondary importance, provided that he does adopt one, and acquires the habit of looking at the problems with which he is occupied as much as possible from a physical point of view. It is no doubt true that these physical theories are liable to imply more than is justified by the analytical theory they are used to illustrate. This however is not important if we remember that the object of such theories is suggestion and not demonstration. Either Experiment or rigorous Analysis must always be the final Court of Appeal; it is the province of these physical theories to supply cases to be tried in such a court. Chapter II is devoted to the consideration of the discharge of electric- ity through gases; Chapter III contains an account of the application of Schwarz’s method of transformation to the solution of two-dimensional problems in Electrostatics. The rest of the book is chiefly occupied with the consideration of the properties of alternating currents; the experiments of Hertz and the development of electric lighting have made the use of these currents, both for experimental and commercial purposes, much more gen- eral than when Maxwell’s Treatise was written; and though the principles which govern the action of these currents are clearly laid down by Maxwell, they are not developed to the extent which the present importance of the subject demands. Chapter IV contains an investigation of the theory of such currents when the conductors in which they flow are cylindrical or spherical, while in Chapter V an account of Hertz’s experiments on Electromagnetic Waves is given. This Chapter also contains some investigations on the Electro- magnetic Theory of Light, especially on the scattering of light by small metallic particles; on reflection from metals; and on the rotation of the plane of polarization by reflection from a magnet. I regret that it was only when this volume was passing through the press that I became acquainted with a valuable paper by Drude (Wiedemann’s Annalen, 46, p. 353, 1892) PREFACE vii on this subject. Chapter VI mainly consists of an account of Lord Rayleigh’s inves- tigations on the laws according to which alternating currents distribute themselves among a network of conductors; while the last Chapter con- tains a discussion of the equations which hold when a dielectric is moving in a magnetic field, and some problems on the distribution of currents in rotating conductors. I have not said anything about recent researches on Magnetic Induction, as a complete account of these in an easily accessible form is contained in Professor Ewing’s ‘Treatise on Magnetic Induction in Iron and other Metals.’ I have again to thank Mr. Chree, Fellow of King’s College, Cambridge, for many most valuable suggestions, as well as for a very careful revision of the proofs. J. J. THOMSON. CONTENTS CHAPTER I. ELECTRIC DISPLACEMENT AND FARADAY TUBES OF FORCE. Art. Page 1. Electric displacement . . . . . . . . . . . . . . . . . 1 2. Faraday tubes . . . . . . . . . . . . . . . . . . . . 1 3. Unit Faraday tubes . . . . . . . . . . . . . . . . . . 2 4. Analogy with kinetic theory of gases . . . . . . . . . . . 3 5. Reasons for taking tubes of electrostatic induction as the unit 4 6. Energy in the electric field . . . . . . . . . . . . . . . 4 7. Behaviour of Faraday tubes in a conductor . . . . . . . . 5 8. Connection between electric displacement and Faraday tubes . 5 9. Rate of change of electric polarization expressed in terms of the velocity of Faraday tubes . . . . . . . . . . . . . . 6 10. Momentum due to Faraday tubes . . . . . . . . . . . . 8 11. Electromotive intensity due to induction . . . . . . . . . 9 12. Velocity of Faraday tubes . . . . . . . . . . . . . . . 10 13. Systems of tubes moving with different velocities . . . . . . 11 14. Mechanical forces in the electric field . . . . . . . . . . . 14 15. Magnetic force due to alteration in the dielectric polarization . 15 16. Application of Faraday tubes to find the magnetic force due to a moving charged sphere . . . . . . . . . . . . . . . 15 17. Rotating electrified plates . . . . . . . . . . . . . . . 23 18. Motion of tubes in a steady magnetic field . . . . . . . . 28 19. Induction of currents due to changes in the magnetic field . . 31 20. Induction due to the motion of the circuit . . . . . . . . . 32 CONTENTS ix Art. Page 21. Effect of soft iron in the field . . . . . . . . . . . . . . 33 22. Permanent magnets . . . . . . . . . . . . . . . . . . 34 23. Steady current along a straight wire . . . . . . . . . . . 35 24. Motion of tubes when the currents are rapidly alternating . . 37 25. Discharge of a Leyden jar . . . . . . . . . . . . . . . 37 26. Induced currents . . . . . . . . . . . . . . . . . . . 40 27. Electromagnetic theory of light . . . . . . . . . . . . . 41 28–32. Behaviour of tubes in conductors . . . . . . . . . . 42–45 33. Galvanic cell . . . . . . . . . . . . . . . . . . . . 47 34. Metallic and electrolytic conduction . . . . . . . . . . . 48 CHAPTER II. PASSAGE OF ELECTRICITY THROUGH GASES. 35. Introduction . . . . . . . . . . . . . . . . . . . . . 52 36. Can the molecules of a gas be electrified? . . . . . . . . . 52 37. Hot gases . . . . . . . . . . . . . . . . . . . . . . 53 38. Electric properties of flames . . . . . . . . . . . . . . 56 39. Effect of ultra-violet light on the discharge . . . . . . . . 56 40. Electrification by ultra-violet light . . . . . . . . . . . . 58 41. Disintegration of the negative electrode . . . . . . . . . . 58 42. Discharge of electricity from illuminated metals . . . . . . 59 43. Discharge of electricity by glowing bodies . . . . . . . . . 61 44. Volta-potential . . . . . . . . . . . . . . . . . . . . 62 45. Electrification by sun-light . . . . . . . . . . . . . . . 64 46. ‘Electric Strength’ of a gas . . . . . . . . . . . . . . . 67 47. Effect of the nature of the electrodes on the spark length . . 67 48. Effect of curvature of the electrodes on the spark length . . . 67 49. Baille’s experiments on the connection between potential differ- ence and spark length . . . . . . . . . . . . . . . . 68 50. Liebig’s on the same subject . . . . . . . . . . . . . . 70 51. Potential difference expressed in terms of spark length . . . . 72 52–53. Minimum potential difference required to produce a spark 72–73 54–61. Discharge when the field is not uniform . . . . . . . 75–82 62–65. Peace’s experiments on the connection between pressure and spark potential . . . . . . . . . . . . . . . . . 83–85 [...]... both to itself and to its direction of motion, whose magnitude is proportional to the component of the velocity at right angles to the direction of the tube The magnetic force and the rotation from the direction of motion to that of the tube at any point are related like translation and rotation in a right-handed screw 10.] The motion of these tubes involves kinetic energy, and this kinetic energy is... hypothesis has the advantage of indicating very clearly why polarization and conduction currents produce similar mechanical and magnetic effects For the mechanical effects and the magnetic forces at any point in the field are due to the motion of the Faraday tubes at that point, and any alteration in the polarization involves motion of these tubes just as much as does an ordinary conduction current 16.] We shall... DISPLACEMENT AND FARADAY TUBES OF FORCE 1.] The in uence which the notation and ideas of the fluid theory of electricity have ever since their introduction exerted over the science of Electricity and Magnetism, is a striking illustration of the benefits conferred upon this science by a concrete representation or ‘construibar vorstellung’ of the symbols, which in the Mathematical Theory of Electricity. .. is in motion, the electromotive intensity is at right angles both to the resultant magnetic induction and to the mean velocity of the tubes, and is equal in magnitude to the product of these two quantities into the sine of the angle between them We see from the preceding equations that there may be a resultant magnetic force due to the motion of the positive tubes in one direction and the negative ones... circuit Substituting the preceding values for dZ/dy − dY /dz, &c., we see that the line integral of the electromotive intensity round a closed circuit is equal to the rate of diminution in the number of lines of magnetic induction passing through the circuit Hence the preceding view of the origin of magnetic force leads to Faraday’s rule for the induction of currents by the alteration of the magnetic... polarization, the direction of motion and the magnetic force, are mutually at right angles; their relative disposition is shown in Fig 1 Collecting the preceding results, we see that when a Faraday tube is in motion it is accompanied by (1) a magnetic force right angles to the tube and to the direction in which it is moving, (2) a momentum at right angles to the tube and to the magnetic induction, (3)... circuits or else begin and end on atoms, all tubes that are not closed being tubes that stretch in the ether along lines either straight or curved from one atom to another When the length of the tube connecting two atoms is comparable with the distance between the atoms in a molecule, the atoms are said to be in chemical combination; when the tube connecting the atoms is very much longer than this, the... 527–529 429 Wheatstone’s bridge with alternating currents 530 430–432 Combination of self-induction and capacity 532–534 432* Effect of two adjacent vibrators on each other’s periods 535 CHAPTER VII ELECTROMOTIVE INTENSITY IN MOVING BODIES 433 Equations of electromotive intensity for moving bodies 538 434–439 Sphere rotating in a symmetrical magnetic field 539–546 440 Propagation of light through... Experiments on electrical oscillations 328 293–297 General investigation of time of vibration of a condenser 329–336 298–299 Vibrations along wires in multiple arc 337–340 300 Time of oscillations on a cylindrical cavity 340 301 On a metal cylinder surrounded by a dielectric 343 302 State of the field round the cylinder 346 303 Decay of currents in. .. magnetic induction, (3) an electromotive intensity at right angles to the direction of motion and to the magnetic induction; this always tends to make the tube set itself at right angles to the direction in which it is moving Thus in an isotropic medium in which there is no free electricity and consequently no electromotive intensities except those which arise from the motion of the tubes, the tubes set themselves . RESEARCHES ELECTRICITY, MAGNETISM *** NOTES ON RECENT RESEARCHES IN ELECTRICITY AND MAGNETISM INTENDED AS A SEQUEL TO PROFESSOR CLERK-MAXWELL’S TREATISE ON ELECTRICITY AND MAGNETISM BY J. J. THOMSON,. License included with this eBook or online at www.gutenberg.net Title: Notes on Recent Researches in Electricity and Magnetism Intended as a Sequel to Professor Clerk-Maxwell’s Treatise on Electricity. magnetic field, and some problems on the distribution of currents in rotating conductors. I have not said anything about recent researches on Magnetic Induction, as a complete account of these in an easily