The origin of this identification is apparent from equation 3.
Maxwell was well aware of the empirical basis of Ohm's law in contrast to the equations of electromagnetic induction. As already mentioned, one of his first successful projects as Cavendish Professor was to establish Ohm's law with much improved precision. The final section of this part of the paper is the determination of the various forms of energy associated with the fields. He starts again with the electromagnetic momentum, or vector potential, A x , A y , A z and finds the total energy from the expression.
The total energy can be related to the total energy existing in the fields themselves:.sireporgentgec.gq
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.
Maxwell's next task is to show how these expressions for the various fields lead to the known laws of forces between the various electromagnetic entities. Note that these force laws had not been explicitly included in the formulation of the equations of electromagnetism. In this part, he derives from the field equations the known laws of force of a conductor moving through a magnetic field, the mechanical force on a magnet and the force on an electrified body.
The last section of this part involves trying to apply the same techniques to understand the laws of gravity. Here, Maxwell hits the problem of the universal attractive force of gravity which results in negative values for the energy of a gravitating system. This section is concerned with the determination of the capacity and absorption of capacitors of various construction. This was an issue of considerable importance for the laying of long lengths of submarine telegraph cables, highlighted by the failure of the project to lay the first transatlantic telegraph cable in The meeting of the British Association had appointed a committee to oversee the determination of fundamental standards and Maxwell joined the Committee in , soon after the publication of his papers on electromagnetism of — He was deeply involved in testing his theory by precise experiment, in particular, the determination of the ratio of electrostatic to electromagnetic units of electric charge.
The activities of the Committee became much more mathematical and theoretical, playing directly to Maxwell's strengths. He set about supervising the design and construction of apparatus to make a very accurate determination of the ohm with his colleagues Balfour Stewart and Fleeming Jenkin at King's College London [ 31 ]. The success of these experiments convinced the Committee that the absolute value of the ohm determined by this and similar techniques was the clearly preferred standard.
The work on standards fragmented in subsequent years, but Maxwell maintained his strong interest and leading role in the subject and made it one of the central themes of the research programme of the new Cavendish Laboratory in The result was that the work on determining the absolute standard of resistance was transferred from the Kew Observatory to the Cavendish. This work was to remain one of the central roles of the Cavendish until it was taken over by the National Physical Laboratory on its foundation in Part VI is another memorable episode in this paper.
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Maxwell now seeks to determine whether or not the waves which can be propagated through any material medium are consistent with the postulate that light can be identified with electromagnetic waves. The analysis looks almost identical to that which appears in all modern standard texts on electromagnetism. Setting the conduction terms to zero, he derives the equations for the propagation of electromagnetic waves in the x , y , z directions in a matter of a page or so:.
This wave consists entirely of magnetic disturbances, the direction of magnetization being in the plane of the wave. No magnetic disturbance whose direction of magnetization is not in the plane of the wave can be propagated as a plane wave at all. Hence magnetic disturbances propagated through the electromagnetic field agree with light in this, that the disturbance at any point is transverse to the direction of propagation, and such waves may have all the properties of polarized light. These figures also agreed within experimental error with the value of the speed of light determined from the astronomical aberration of light rays.
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Next, Maxwell goes on to show that the refractive index of a non-conducting material n is given by the square root of the specific inductive capacity of the medium. He writes. Maxwell then makes a preliminary exploration of the case of anisotropic crystalline materials. The next application is the relation between electrical resistance and the transparency of materials. The proportion of incident intensity of light transmitted through the thickness x is. If R is the resistance of a sample of the material of thickness is x , breadth b and length l , then.
The final part of the paper concerns the accurate estimation of the coefficients of electromagnetic induction. This might seem a descent from the heights of parts III, IV and VI of the paper, but these calculations were of central importance for the absolute determination of the ohm, one of Maxwell's preoccupations for the rest of his life.
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Suffice to say that Maxwell describes in some detail the various ways in which self and mutual inductances could be measured, in the context of the experiments which he and his colleagues were carrying out at King's College London and which were contained in the Report to the Committee of the British Association. The considerations were to find their application in the meticulous experiments of Rayleigh and colleages [ 32 , 33 ] in their determination of the absolute value of the ohm after Maxwell's death. The identification of light with electromagnetic radiation was a triumph, providing a physical foundation for the wave theory of light, which could successfully account for the phenomena of reflection, refraction, polarization and so on.
It is striking, however, how long it took for Maxwell's deep insights to become generally accepted by the community of physicists. He elaborated the theory in his great Treatise on Electricity and Magnetism as soon as he had settled back at his home at Glenlair in the Dumfries and Galloway region of southern Scotland in It is significant that, while he was writing the Treatise , he was also an examiner for the Cambridge Mathematical Tripos and realized the dire need for suitable textbooks.
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The two-volume Treatise is, however, unlike many of the other great treatises such as Newton's Principia in that it is not a systematic presentation of the subject but a work in progress, reflecting Maxwell's own approach to these researches. In a later conversation, Maxwell remarked that the aim of the Treatise was not to expound his theory finally to the world, but to educate himself by presenting a view of the stage he had reached. Disconcertingly, Maxwell's advice was to read the four parts of the Treatise in parallel rather than in sequence.
The advantage of this approach was that Maxwell laid out clearly his own perception of the physical content of the theory and also how it could be confronted by precise experiment.
These topics were strongly influenced by his work for the British Association committee on fundamental standards. He devotes a large part of the Treatise to basic measurements and electrical apparatus, in the process providing many experimental challenges which would be taken up by the research students in the Cavendish Laboratory. For example, he analyses five methods of making absolute determinations of the standard of resistance, occupying the whole of ch.
As summarized by Peter Harman, Maxwell emphasizes the expression of physical quantities free from direct representation by a mechanical model. This needed new mathematical approaches to electromagnetism, including quaternions, integral theorems such as Stokes' theorem, topological concepts and Lagrangian—Hamiltonian methods of analytic dynamics. One of the most important results appears in section of Volume 2 in which Maxwell works out the pressure which radiation exerts on a conductor on the basis of electromagnetic theory. This result was to be used by Boltzmann in his paper of in which he derived the Stefan—Boltzmann law from classical thermodynamics.
Published in , the Treatise had an immediate impact and, together with Thomson and Tait's Treatise on Natural Philosophy , provided students with a comprehensive overview of both experimental and theoretical physics. Maxwell was remarkably modest about his contribution. But the problems were much deeper. Not only was Maxwell's theory complex, but the discovery of the equations for the electromagnetic field also required a major shift in perspective for physicists of the late nineteenth century.
It is worth quoting Dyson a little further. There were other reasons, besides Maxwell's modesty, why his theory was hard to understand. He replaced the Newtonian universe of tangible objects interacting with one another at a distance by a universe of fields extending through space and only interacting locally with tangible objects.
The notion of a field was hard to grasp because fields are intangible.
The scientists of that time, including Maxwell himself, tried to picture fields as mechanical structures composed of a multitude of little wheels and vortices extending throughout space. These structures were supposed to carry the mechanical stresses that electric and magnetic fields transmitted between electric charges and currents. To make the fields satisfy Maxwell's equations, the system of wheels and vortices had to be extremely complicated.
If you try to visualize the Maxwell theory with such mechanical models, it looks like a throwback to Ptolemaic astronomy with planets riding on cycles and epicycles in the sky. It does not look like the elegant astronomy of Newton. Maxwell died in before direct experimental evidence was obtained for the existence of electromagnetic waves. The matter was finally laid to rest ten years after Maxwell's death in a classic series of experiments by Heinrich Hertz, almost 30 years after Maxwell had identified light with electromagnetic radiation.
Hertz's great monograph On Electric Waves [ 34 ] sets out beautifully his remarkable set of experiments. Hertz found that he could detect the effects of electromagnetic induction at considerable distances from his apparatus.