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A Treatise on Electricity and Magnetism

From Wikipedia, the free encyclopedia

A Treatise on Electricity and Magnetism
Title page from volume I of Maxwell's masterwork
AuthorJames Clerk Maxwell
CountryEngland
LanguageEnglish
Subject
Genre
PublisherOxford University Press
Publication date
1873
TextA Treatise on Electricity and Magnetism at Wikisource

A Treatise on Electricity and Magnetism is a two-volume treatise on electromagnetism written by James Clerk Maxwell in 1873. Maxwell was revising the Treatise for a second edition when he died in 1879. The revision was completed by William Davidson Niven for publication in 1881. A third edition was prepared by J. J. Thomson for publication in 1892.

The treatise is said to be notoriously hard to read, containing plenty of ideas but lacking both the clear focus and orderliness that may have allowed it catch on more easily.[1] It was noted by one historian of science that Maxwell's attempt at a comprehensive treatise on all of electrical science tended to bury the important results of his work under "long accounts of miscellaneous phenomena discussed from several points of view."[1] He goes on to say that, outside the treatment of the Faraday effect, Maxwell failed to expound on his earlier work, especially the generation of electromagnetic waves and the derivation of the laws governing reflection and refraction.[1]

Maxwell introduced the use of vector fields, and his labels have been perpetuated:

A (vector potential), B (magnetic induction), C (electric current), D (displacement), E (electric field – Maxwell's electromotive intensity), F (mechanical force), H (magnetic field – Maxwell's magnetic force).[2]

Maxwell's work is considered an exemplar of rhetoric of science:[3]

Lagrange's equations appear in the Treatise as the culmination of a long series of rhetorical moves, including (among others) Green's theorem, Gauss's potential theory and Faraday's lines of force – all of which have prepared the reader for the Lagrangian vision of a natural world that is whole and connected: a veritable sea change from Newton's vision.

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Transcription

Now I'm going to blow your mind I'm going to make you see something that you won't believe and so try to follow step-by-step leading up to this unbelievable and very non-intuitive result I have here a battery and the battery has an EMF of 1 V here is a resistor R1 which is 100 ohms and here is a resistor R2 which is 900 ohms and I'm asking you what is the current that is flowing around you will laugh at me, you will say that is almost an insult I wish you'd given *that* problem at the first exam because E equals the current that is going to run divided by R1 + R2 Oh, my goodness, what did I do ha ha ha I forgot Ohm's law E = IR remember? not I/R so R1 + R2 should go upstairs and everything that follows is correct so you don't have to worry about that this was just a big slip of the pen and so the current I is 10^-3 A 1 mA big deal easy current is going to flow like this fine lets call this point D and call this point A and I ask what is the potential difference between D and A you will be equally insulted VD - VA you apply Ohm's law you say that's this current times R2 absolutely I X R2 so that is +0.9 V now I say to you, well suppose you had gone this way then you would have said well I find the same thing of course Kirchhoff's rule so indeed if you go VD - VA and you go this way then notice this battery this point is 1 V above this point but you have in the resistor here you have a voltage drop according to Ohm's law and the current times 100 ohms gives you a one-tenth voltage drop here so VD - VA is the 1 V from the battery - I X R1 and that is +0.9 V what a waste of time that we did it twice and we found the same result soooo... I connect here a voltmeter the voltmeter is connected to point D and to point A and I ask you what're you going to see? the answer is +0.9 V and you will provided that the plus sign of the voltmeter is connected here and the minus sign of the voltmeter there voltmeters are polarity sensitive this is fine Kirchhoff's rule works the close loop integral from E dot dL going from D back to D is zero so far, so good now hold on to your chairs I'm going to take the battery out who needs the battery? I'm going to replace the battery by a solenoid which you see right here and this solenoid when I switch it on is creating an increasing magnetic field only here and lets assume that an increasing magnetic field is coming out of the board and that it is increasing Lenz's law will immediately tell you in what direction the current is if this magnetic field is increasing towards you the current will be in this direction the magnetic flux changes d\phi/dt at a particular moment in time happens to be 1 V an amazing coincidence, isn't it? E induced at a moment in time is 1 V but now I ask you what is the current? well, you will be surprised that I even have the courage to ask you that because Ohm's law holds the induced EMF is 1 V and R1 + R2 is still 1000 ohms so 10^-3 A I really make a nuisance of myself when I say what is VD - VA and you get annoyed at me and you say, look the current I through R2 Ohm's law V equals IR, +0.9 V and then I say but now suppose we go the other the other side and we want to know now what VD - VA is and now it's not so simple because there's no battery and so now when I go from D to A I don't have this one and therefore I now find -0.1 V I find a totally different answer I attach a voltmeter here that voltmeter will show me +0.9 V now I attach a voltmeter here the same one I flip it over it's connected between point D and point A it will read -0.1 V this voltmeter which is connected between D and A reads +0.9 this voltmeter which is connected to D and A reads -0.1 the two values are different and I placed on the web a lecture supplement which goes through the derivation step-by-step which will convince you that indeed this is what is happening why we can't digest this so easily is we don't know how to handle non-conservative fields if you have a non-conservative field then if you go from A to D of E dot dL or from D to A for that matter doesn't matter the answer depends on the path it's no longer independent of the path and so if here is D and here is A and we go this way you find 0.9 V plus if you go this way you find -0.1 V Faraday has no problems with that Kirchhoff has a problem with that but who cares about Kirchhoff? Faraday is the law that matters because Faraday's law always holds because if d\phi/dt is 0 then you get Kirchhoff's Kirchhoff's rule is simply a special case of Faraday's law and Faraday's law always holds so Kirchhoff is for the birds and Faraday is not suppose you go from D to A and back to D well we know that VD - VA if we go through... if we go this way through R2 we know that VD - VA is +0.9 V now we are at A and we go through the left side back to D so we now have VA - VD that of course is now +0.1 V because remember if VD - VA is -0.1 then VA - VD is plus and so we add them up and we find that VD - VD is plus 1 V Kirchoff said has to be 0 because I'm back at the same potential where I was before Faraday says uh uh I'm sorry you can't do that that 1 volt is exactly that EMF of 1 V that is the closed loop integral of E dot dL around that loop it's no longer 0 SUBTITLES: zer0s0und

Contents

Preliminary On the Measurement of Quantities, A Treatise on Electricity and Magnetism (1873)
Preliminary On the Measurement of Quantities, A Treatise on Electricity and Magnetism (1873)

Preliminary. On the Measurement of Quantities.

Part I. Electrostatics.

  1. Description of Phenomena.
  2. Elementary Mathematical Theory of Electricity.
  3. On Electrical Work and Energy in a System of Conductors.
  4. General Theorems.
  5. Mechanical Action Between Two Electrical Systems.
  6. Points and Lines of Equilibrium.
  7. Forms of Equipotential Surfaces and Lines of Flow.
  8. Simple Cases of Electrification.
  9. Spherical Harmonics.
  10. Confocal Surfaces of the Second Degree.
  11. Theory of Electric Images.
  12. Conjugate Functions in Two Dimensions.
  13. Electrostatic Instruments.

Part II. Electrokinematics.

  1. The Electric Current.
  2. Conduction and Resistance.
  3. Electromotive Force Between Bodies in Contact.
  4. Electrolysis.
  5. Electrolytic Polarization.
  6. Mathematical Theory of the Distribution of Electric Currents.
  7. Conduction in Three Dimensions.
  8. Resistance and Conductivity in Three Dimensions.
  9. Conduction through Heterogeneous Media.
  10. Conduction in Dielectrics.
  11. Measurement of the Electric Resistance of Conductors.
  12. Electric Resistance of Substances.

Part III. Magnetism

  1. Elementary Theory of Magnetism.
  2. Magnetic Force and Magnetic Induction.
  3. Particular Forms of Magnets.
  4. Induced Magnetization.
  5. Magnetic Problems.
  6. Weber's Theory of Magnetic Induction.
  7. Magnetic Measurements.
  8. Terrestrial Magnetism.

Part IV. Electromagnetism.

  1. Electromagnetic Force.
  2. Mutual Action of Electric Currents.
  3. Induction of Electric Currents.
  4. Induction of a Current on Itself.
  5. General Equations of Dynamics.
  6. Application of Dynamics to Electromagnetism.
  7. Electrokinetics.
  8. Exploration of the Field by means of the Secondary Circuit.
  9. General Equations.
  10. Dimensions of Electric Units.
  11. Energy and Stress.
  12. Current-Sheets.
  13. Parallel Currents.
  14. Circular Currents.
  15. Electromagnetic Instruments.
  16. Electromagnetic Observations.
  17. Electrical Measurement of Coefficients of Induction.
  18. Determination of Resistance in Electromagnetic Measure.
  19. Comparison of Electrostatic With Electromagnetic Units.
  20. Electromagnetic Theory of Light.
  21. Magnetic Action on Light.
  22. Electric Theory of Magnetism.
  23. Theories of Action at a distance.

Reception

Reviews

On April 24, 1873, Nature announced the publication with an extensive description and much praise.[4] When the second edition was published in 1881, George Chrystal wrote the review for Nature.[5]

Pierre Duhem published a critical essay outlining mistakes he found in Maxwell's Treatise.[6] Duhem's book was reviewed in Nature.[7]

Comments

Hermann von Helmholtz (1881): "Now that the mathematical interpretations of Faraday's conceptions regarding the nature of electric and magnetic force has been given by Clerk Maxwell, we see how great a degree of exactness and precision was really hidden behind Faraday's words…it is astonishing in the highest to see what a large number of general theories, the mechanical deduction of which requires the highest powers of mathematical analysis, he has found by a kind of intuition, with the security of instinct, without the help of a single mathematical formula."[8]

Oliver Heaviside (1893):”What is Maxwell's theory? The first approximation is to say: There is Maxwell's book as he wrote it; there is his text, and there are his equations: together they make his theory. But when we come to examine it closely, we find that this answer is unsatisfactory. To begin with, it is sufficient to refer to papers by physicists, written say during the first twelve years following the first publication of Maxwell's treatise to see that there may be much difference of opinion as to what his theory is. It may be, and has been, differently interpreted by different men, which is a sign that is not set forth in a perfectly clear and unmistakable form. There are many obscurities and some inconsistencies. Speaking for myself, it was only by changing its form of presentation that I was able to see it clearly, and so as to avoid the inconsistencies. Now there is no finality in a growing science. It is, therefore, impossible to adhere strictly to Maxwell's theory as he gave it to the world, if only on account of its inconvenient form.[9][10]

Alexander Macfarlane (1902): "This work has served as the starting point of many advances made in recent years. Maxwell is the scientific ancestor of Hertz, Hertz of Marconi and all other workers at wireless telegraphy.[11]

Oliver Lodge (1907) "Then comes Maxwell, with his keen penetration and great grasp of thought, combined with mathematical subtlety and power of expression; he assimilates the facts, sympathizes with the philosophic but untutored modes of expression invented by Faraday, links the theorems of Green and Stokes and Thomson to the facts of Faraday, and from the union rears the young modern science of electricity..."[12]

E. T. Whittaker (1910): "In this celebrated work is comprehended almost every branch of electric and magnetic theory, but the intention of the writer was to discuss the whole from a single point of view, namely, that of Faraday, so that little or no account was given of the hypotheses that had been propounded in the two preceding decades by the great German electricians...The doctrines peculiar to Maxwell ... were not introduced in the first volume, or in the first half of the second."[13]

Albert Einstein (1931): "Before Maxwell people conceived of physical reality – in so far as it is supposed to represent events in nature – as material points, whose changes consist exclusively of motions, which are subject to total differential equations. After Maxwell they conceived physical reality as represented by continuous fields, not mechanically explicable, which are subject to partial differential equations. This change in the conception of reality is the most profound and fruitful one that has come to physics since Newton; but it has at the same time to be admitted that the program has by no means been completely carried out yet."[14]

Richard P. Feynman (1964): "From a long view of the history of mankind—seen from, say, ten thousand years from now—there can be little doubt that the most significant event of the 19th century will be judged as Maxwell's discovery of the laws of electrodynamics. The American Civil War will pale into provincial insignificance in comparison with this important scientific event of the same decade."[15]

L. Pearce Williams (1991): "In 1873, James Clerk Maxwell published a rambling and difficult two-volume Treatise on Electricity and Magnetism that was destined to change the orthodox picture of physical reality. This treatise did for electromagnetism what Newton's Principia had done for classical mechanics. It not only provided the mathematical tools for the investigation and representation of the whole of electromagnetic theory, but it altered the very framework of both theoretical and experimental physics. Although the process had been going on throughout the nineteenth century, it was this work that finally displaced action at a distance physics and substituted the physics of the field."[16]

Mark P. Silverman (1998) "I studied the principles on my own – in this case with Maxwell's Treatise as both my inspiration and textbook. This is not an experience that I would necessarily recommend to others. For all his legendary gentleness, Maxwell is a demanding teacher, and his magnum opus is anything but coffee-table reading...At the same time, the experience was greatly rewarding in that I had come to understand, as I realized much later, aspects of electromagnetism that are rarely taught at any level today and that reflect the unique physical insight of their creator.[2]: 202 

Andrew Warwick (2003): "In developing the mathematical theory of electricity and magnetism in the Treatise, Maxwell made a number of errors, and for students with only a tenuous grasp of the physical concepts of basic electromagnetic theory and the specific techniques to solve some problems, it was extremely difficult to discriminate between cases where Maxwell made an error and cases where they simply failed to follow the physical or mathematical reasoning."[17]

See also

References

  1. ^ a b c Bruce J. Hunt (1991) The Maxwellians, page 13
  2. ^ a b Mark P. Silverman (1998) Waves and Grains: reflections on light and learning, pages 205, 6, Princeton University Press ISBN 0-691-00113-8
  3. ^ Thomas K. Simpson (2010) Maxwell's Mathematical Rhetoric: rethinking the Treatise on Electricity and Magnetism, page xiii, Santa Fe, New Mexico: Green Lion Press
  4. ^ "A Treatise on Electricity and Magnetism". Nature. 7 (182): 478–480. 24 April 1873. Bibcode:1873Natur...7..478.. doi:10.1038/007478a0. ISSN 1476-4687. S2CID 10178476.
  5. ^ George Chrystal (1882) Review: 2nd edition, link from Nature
  6. ^ Pierre Duhem (1902). Les Théories Électriques de J. Clerk Maxwell: Étude Historique et Critique. Paris: A. Hermann
  7. ^ W. McF. Orr (1902) "A French Critic of Maxwell", Nature 17 April 1902
  8. ^ Hermann Helmholtz (1881) "On the modern development of Faraday's conception of electricity", Faraday Lecture at the Royal Society
  9. ^ Oliver Heaviside (1893) Electromagnetic Theory, v. 1, Preface, p. vii, link from Internet Archive
  10. ^ The Maxwellians, page 201
  11. ^ Alexander Macfarlane (1916) Lectures on Ten British Physicists of the Nineteenth Century, link from Internet Archive
  12. ^ Oliver Lodge (1907) Modern Views of Electricity, 3rd edition, page 24, Macmillan & Company
  13. ^ E. T. Whittaker (1910) A History of the Theories of Aether and Electricity, page 300
  14. ^ Einstein, Albert (1931). "Maxwell's Influence On The Evolution Of The Idea Of Physical Reality". James Clerk Maxwell: A Commemoration Volume. C.U.P. Archived from the original on 14 July 2014. Retrieved 7 July 2014.
  15. ^ Bruce J. Hunt (1991) The Maxwellians, page 1, Cornell University Press ISBN 0-8014-2641-3. Source The Feynman Lectures on Physics (1964) 2:1.11
  16. ^ L. Pearce Williams (1991) Preface to The Maxwellians
  17. ^ Andrew Warwick (2003) Masters of Theory: Cambridge and the Rise of Mathematical Physics, chapter 6: Making sense of Maxwell's Treatise on Electricity and Magnetism in Mid-Victorian Cambridge, pp. 286–356, quote p. 297, University of Chicago Press ISBN 0-226-87374-9

Further reading

External links

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