He said: "Faraday's mind sees the magnetic field lines running through the whole space, while mathematicians only see the center of attraction in the distance;" Faraday saw the medium, mathematicians only saw the distance; Faraday thinks that phenomenon is a real action in a medium, while mathematicians are satisfied with discovering the over-distance force acting on electrofluids. "
Faraday's line of force thought deeply attracted Maxwell and left a very deep impression on him. In later memories, he talked about how he "read Faraday's description of electromagnetic induction experiment with deep reverence and piety" and said: "Faraday's experiment provided a wonderful example of the existence of magnetic lines of force, which made me believe that magnetic lines of force are actually things." Later, Maxwell made a further confession to this point in the General Theory of Electromagnetic Fields. He wrote: "I mainly undertake the writing of this book with the desire to provide a mathematical basis for Faraday's thought."
Maxwell gave an accurate mathematical description of Faraday's magnetic field lines through analogy, and based on electromagnetic experiments and dynamics principles, through his own efforts, he finally established the electromagnetic field equation. The establishment of Maxwell's electromagnetic field theory has established rich methods for us.
(1) Reveals the internal relations of physical phenomena through analogy.
Analogy usually refers to studying the similarity of two kinds of objects in nature or relationship, and inferring on this basis. From the known attributes and relationships of one kind of objects, we can infer some unknown attributes and relationships of another kind of objects, so it is a special way of thinking. It plays an important role in scientific research, enlightening thinking and opening the way for new scientific exploration.
Maxwell pointed out: "Physical analogy is to use the partial similarity between one scientific law and another to explain the other." "Analogy is based on the similarity of two laws in mathematical form." Analogy can communicate research methods in different fields, provide a medium between analyzing abstract forms and assumptions, inspire new physical ideas, and help people understand and discover some physical processes and laws to be studied.
Maxwell was inspired by the analogy of W. Thomson (1824- 1907, that is, Kelvin, L.). In "On Faraday's Line of Force", in order to accurately deal with Faraday's concept, he compared the line of force with the streamline of incompressible fluid by analogy. Because the velocity direction of fluid is the same as the tangent direction of streamline and inversely proportional to the cross-sectional area of flow tube, the magnitude of force is inversely proportional to the cross-sectional area of force tube, and a geometric model representing both the magnitude and direction of force is obtained. Because in an isotropic infinite homogeneous medium, the velocity at the distance from the fluid source F is inversely proportional to the square of the distance, the electric field intensity generated by the point charge corresponds to the velocity generated by the fluid source in the fluid. From these analogies, Maxwell concluded that the pressure in the fluid corresponds to the electrostatic potential, and the pressure gradient in the fluid corresponds to the potential gradient. He clearly pointed out that because of the existence of resistance in the conductor, in order to produce stable current in the closed loop, there must be electromotive force.
Maxwell compared the electric field with the velocity field. Based on the precise mathematical treatment of Faraday's magnetic field lines, the relationship between electromagnetic quantities was established according to some basic principles of electromagnetism (such as Ohm's Law and Ampere's Loop Theorem), and the changes of electric field and magnetic field in space were described by clearly defined quantities such as flux, circulation, divergence and curl, and the basic equations of electromagnetic field were established.
(2) Establish electromagnetic field theory with precise mathematical language;
Concise and accurate mathematical language is an important form of expressing scientific concepts and theories, a requirement of scientific development and one of the signs of scientific maturity. As Marx said: "A science can only be perfect if it successfully uses mathematics." With the progress of science and technology, the development of modern science is becoming more and more quantitative. Only quantitative mathematical description can stand the test of experiment in quantity, and we can also find the deficiency of theory and improvement methods from the subtle differences in quantity. Maxwell finally expressed his thoughts, models and images as the basic equations of electromagnetic field with his profound mathematical foundation and skillful mathematical skills.
In On Faraday's Magnetic Field Lines, Maxwell expressed Faraday's concepts of electric tension and magnetic field lines in mathematical language, introduced the concept of induced electric field, and deduced the relationship between induced electric field and changing magnetic field. In The Line of Physical Forces, with the help of molecular vortex model, he deduced the formula of wave propagation in vortex matter at the speed of light, revealed the relationship between electromagnetic phenomena and light phenomenon, and predicted that light is electromagnetic wave. In the theory of electromagnetic field dynamics, he established the concept of field, introduced the concept of displacement current, deduced the total current theorem according to the basic principles of electromagnetism (Gauss theorem and law of charge conservation), and finally established the basic equation of electromagnetic field.
Describing physical concepts with precise and quantitative mathematical language is fully reflected in Maxwell's works. He used the axiomatic method of mathematics to comprehensively sort out the achievements of predecessors and make the theory systematic, formal and standardized. His electromagnetic field equation is a model of axiomatization of scientific theory. Einstein and infeld commented in the book Evolution of Physics: "The formulation of these equations is one of the most important events in physics since Newton's time, not only because of its rich content, but also because it constitutes a model of a new law."
It is worth pointing out that Maxwell, as a master of mathematical physics, attaches great importance to the combination of mathematical theory and physical experiment. He said: "The knowledge of physical science obtained through the combination of mathematical analysis and experimental research is more solid, beneficial and firm than the knowledge that a simple experimenter or a simple mathematician can have." 1874, he founded the world-famous Cavendish laboratory, and personally served as the first director, establishing a good style of study. In his inaugural speech, he said: "The usual tools-pen, ink and paper-are not enough. We will need more space than the classroom and more area than the blackboard. " This is a severe refutation of the so-called "chalk" physics that was still dominant in conservative British universities at that time. He regarded the laboratory as a "school of scientific criticism" and advocated the use of collective strength to complete scientific research. This is the basic form and bud of future natural science research methods.
Maxwell and Faraday are two superstars in the history of modern electromagnetism, and both of them have achieved great success in the field of electromagnetism. Although their scientific methods and styles are quite different, Maxwell did not belittle Faraday's style. He once said: "Because there are different types of human minds, scientific truth should also have different forms of expression. Whether he explains his bright colors in a straightforward physical way or expresses them in simple and innocent symbols, they should be regarded as the same science. " Maxwell maintained a noble character of modesty and prudence all his life. He once thought that compared with Faraday, he was just a pen and wrote Faraday's outstanding scientific thought. Einstein once called them scientific companions, just like Tycho and Kepler in astronomy.
Einstein also profoundly expounded Maxwell's influence on the development of the concept of physical reality. He said: "I believe that there is an independent external world far from the perceptual subject, which is the basis of all natural sciences." But people's concept of physical reality is by no means static. In fact, it has undergone far-reaching changes in the historical process. Einstein pointed out that in Newton's view, particles are the only form and the only representative of reality. This view
It is atomistic and mechanistic in nature. All events should be explained mechanically-that is, they should be interpreted as particle motion in full accordance with Newton's laws of motion. But in Faraday's and Maxwell's view, physics is indeed represented by a continuous field and cannot be explained by mechanics. This change in the concept of reality is the most profound and fruitful change in physics since Newton. Einstein also commented: "Since Newton laid the foundation of theoretical physics, the axiomatic foundation of physics-in other words, our biggest change in the concept of real structure was caused by Faraday and Maxwell's work in electromagnetic phenomena." Planck, the founder of quantum theory, pointed out: "Maxwell's name will always be engraved on the door of classical physicists and shine forever." From his birthplace, he belongs to Edinburgh; Personally, he belongs to Cambridge University; As far as merits are concerned, he belongs to the whole world. "