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Einstein worked at the Princeton Institute for Advanced Studies for many years, and on the wall of his office were portraits of three men, Newton, Faraday and Maxwell, whom he admired most.

James Clark Maxwell, with a long beard, serious manner and bright eyes, has made the most outstanding contributions to electromagnetism, optics, molecular physics, astronomy and many other fields, although he lived only 48 years old.

James Clark Maxwell said that Newton unified the laws of motion in heaven and earth and realized the first great unity in physics, while Maxwell unified electricity, magnetism and light and realized the second great unity in physics. Maxwell and Newton jointly pushed classical physics to its peak.

Maxwell summed up all human understanding of macroscopic electromagnetic phenomena, theoretically established the relationship between electricity and magnetism, and brilliantly predicted electromagnetic waves, which opened the way for the birth of radio electronics and the development of technology. It makes it possible to develop all these modern technologies, such as radio communications, radar, navigation, remote sensing, radio broadcasting, television, computers, mobile phones and so on.

In 1854, Maxwell received a degree in mathematical physics from Trinity College, Cambridge University with honors. Faraday's masterpiece, the Experimental study of electricity, was published in this year, which is a masterpiece summarizing the results of his lifetime study of electromagnetic phenomena. Maxwell noticed that Faraday's account of the experiment was not a matter of fact, but stood at a certain height to reveal the nature of electromagnetic phenomena, and Maxwell was immediately attracted by the novel ideas. He grasped Faraday's two important physical ideas: one is the explanation of the "spaced" interaction between charges and magnets. Faraday introduced the idea of "line of force" and "force-induced tension in space". This idea is the embryonic form of the concept of electric field and magnetic field. The other is that Faraday reveals the corresponding relationship between electricity and magnetism through electromagnetic induction, and enlightens the inherent symmetry of "electric world" and "magnetic world". These two ideas enlighten Maxwell greatly.

To Maxwell's surprise, he couldn't find a mathematical formula in Faraday's thick three-volume masterpiece. Why? As a physicist familiar with theoretical research, Maxwell believes that with mathematics, and only with mathematics can we describe physical phenomena more succinctly and reveal the essence of physics more deeply. While deeply admiring Faraday, he found that Faraday's deficiency, only the height of thought, the lack of concise mathematical expression, the natural lack of theoretical rigor, it can not go far. As Kant said, "in any particular theory, only the part that contains mathematics is the real science."

Maxwell, who was only 23 years old at the time, was determined to supplement Faraday's deficiency and seek the "real science" between electricity and magnetism. A year later, on February 11, 1856, he published the Faraday Line of Power. In this paper, he uses mathematical methods to generalize Faraday's predicted line of force into an equation, so that Faraday's theory has a quantitative mathematical expression, this paper immediately attracted the attention of physics theorists.

Along this line of thinking, Maxwell continues to study the mathematical laws between electricity and magnetism, and its purpose is to dig deeper into the laws of nature and understand the design of nature more deeply.

Five years later, in 1861, he published his second paper on electromagnetism, on the Line of Force in Physics, in the philosophical Journal of the Royal Society of London. In this famous paper, he boldly introduced an epoch-making new concept, which is "displacement current".

The introduction of this new concept not only closes the circuit of charging and discharging capacitors, but also breaks the traditional shackles that only "conducting current" can produce magnetic field. The epoch-making significance of displacement current is not only that, but also reveals the formal perfection and symmetry of electromagnetic law more profoundly because of its introduction.

On this basis, Maxwell established two very concise mathematical formulas, which are two highly abstract differential equations with only a few mathematical symbols, which look symmetrical and simple, but their meanings are very rich, so they are very beautiful. The mathematization of physical laws is not only limited to its simplification, but more importantly, it is deepened. At the same time of mathematization, science is also developing in depth. Maxwell's differential equation not only satisfactorily explains Faraday's law of electromagnetic induction, but also can explain all the electromagnetic phenomena seen so far.

To sum up, it includes two aspects: one is that when the electric field changes, it will cause the magnetic field; the other is when the magnetic field changes, it will produce the electric field, the two are closely related, excite each other and cause and effect each other. It is the mathematization of physical laws that makes Maxwell boldly predict that this alternating electromagnetic field can propagate outward, forming electromagnetic waves that people do not know yet. The shock of this paper to people at that time can be imagined.

On December 8, 1864, Maxwell completed his more important third paper, the Dynamics of electromagnetic Fields. he got a perfect set of mathematical expressions, from which he made an even more amazing discovery. this set of equations unexpectedly expresses a wave equation! When he got this equation, Maxwell had undisguised delight. Restraining his inner excitement, he immediately calculated the propagation velocity of the wave according to the parameters of the wave equation. The result is incredible. The propagation speed of electromagnetic waves is exactly equal to the speed of light! It simply stunned him.

This is a dramatic discovery. After Maxwell mathematized the laws of electromagnetism, he suddenly revealed two shocking secrets: electromagnetic waves exist, and light is electromagnetic waves! At that time, he calculated the speed of light at 310,740,000 meters per second.

Maxwell's famous paper was officially published in the philosophical Journal of the Royal Society of London on January 1, 1865 under the title of "on the electrokinetic theory of electromagnetic fields". In the history of natural science, only when science in one field reaches a certain peak can it be expressed in mathematics. It was the predecessors Coulomb, Oster, Ampere, Faraday and others who developed electromagnetics to commanding heights one by one, which led Maxwell to the peak at last.

In 1873, Maxwell's brilliant masterpiece the Theory of electromagnetism was published. Maxwell summed up the achievements of his predecessors and expressed all the electromagnetic theories in a concise, symmetrical and perfect mathematical form, which is the Maxwell equations that have become the basis of classical electrodynamics. At this point, the numerous and complicated electromagnetic phenomena in the macro world are all summarized into this set of equations, and no electromagnetic phenomenon can escape from this set of equations. Starting from this set of equations, all electromagnetic laws can be deduced.

Maxwell equations can be expressed in two ways. Maxwell equations in integral form are mathematical models that describe electromagnetic fields in a certain volume or area. The expression is:

① is a full current law derived from the Ampere loop law, which means that the line integral of the magnetic field intensity H along an arbitrary closed curve is equal to the total current passing through the defined area of the curve. The first item on the right of the equal sign is the conduction current. The second item is the displacement current.

Formula ② is the expression of Faraday's law of electromagnetic induction, which states that the line integral of the electric field intensity E along an arbitrary closed curve is equal to the negative value of the rate of change of the magnetic flux passing through the area defined by the curve. The closed curve mentioned here does not have to be made up of conductors, it can be a dielectric loop, or even just any closed profile.

③ represents the principle of flux continuity, indicating that for any closed surface, the same number of flux leaves as much as the flux enters the surface. That is, the B line has neither beginning nor terminal; at the same time, it also shows that there is no magnetic charge corresponding to the charge.

Formula ④ is the expression of Gauss law, which shows that under the condition of time variation, the net flux of D from any closed surface should be equal to the sum of all free charges in the volume surrounded by the closed surface.

two。 Maxwell equations in differential form. The differential Maxwell equation is for every point in the field. Using the del operator, you can write them as follows:

Formula ⑤ is the differential form of the total current law, which shows that the curl of the magnetic field intensity H is equal to the total current density at this point, that is, the vortex source of the magnetic field is the total current density, and the displacement current can produce a magnetic field as well as the conduction current.

⑥ is the differential form of Faraday's law of electromagnetic induction, which shows that the curl of the electric field intensity E is equal to the negative value of the time change rate of the magnetic flux density B at this point, that is, the vortex source of the electric field is the time change rate of the magnetic flux density.

Formula ⑦ is the differential form of the principle of flux continuity, which shows that the divergence of flux density B is always equal to zero, that is, the B line has no beginning and no end. That is to say, there is no magnetic charge corresponding to the charge.

⑧ is a generalization of Gauss's law of electrostatic field, that is, under the condition of time-varying, the divergence of potential shift D is still equal to the bulk density of free charge at this point.

In addition to the above four equations, the constitutive relation of the medium is also needed.

In order to finally solve the problem of field quantity. In the formula, ε is the permittivity of the medium, μ is the permeability of the medium, and σ is the conductivity of the medium.

This set of perfect, harmonious and symmetrical equations can be called an exquisite masterpiece. Together with Newtonian mechanics equation, Einstein gravitational field equation, Schrodinger equation and Dirac equation, it pushes physics to the highest level. it contains the most abundant content in the most concentrated and concise mathematical language, reveals the basic structure of the physical world, and becomes the most magnificent poem in physics.

Maxwell's ideas went far beyond the era in which he lived, when people did not believe in the existence of electromagnetic waves and did not believe in his theory. His short life has always been incomprehensible.

In high school, his clothes were not understood, in college, his language was not understood by the listeners, and later, his theory was difficult to find a bosom friend for a long time. His honor was far inferior to that of Faraday, and it was not until many years after his death, when Hertz confirmed the existence of electromagnetic waves, that people realized that he was the first greatest physicist and mathematician since Newton.

In 1931, at the commemoration of Maxwell's centenary, Einstein evaluated his achievements. "it is the most profound and fruitful work in physics since Newton."

Maxwell's achievements in electromagnetism are regarded as "the second great unity of physics" after Isaac Newton. Maxwell is widely regarded as the most influential 19th century physicist in the twentieth century. His contribution to basic natural science is second only to Isaac Newton.

In the history of science, it is said that Newton's unification of the laws of movement in heaven and earth is the first great synthesis, while Maxwell's unification of electricity and light is the second great synthesis.

In the statue of Maxwell built on George Edinburgh Street on October 12, 2009, Maxwell holds a colorful plate that confirms that white is a compound color, nearly a century after it was left out in the cold. At the end of 1999, at the end of the millennium, the British magazine physical World selected the 10 greatest physicists of all time, his name becoming the third person after Einstein and Newton.

Comprehensive since: book "365 days in the History of Science", Maxwell equations Baidu Encyclopedia Book author: Wei Fengwen Wu Yi part of the picture source network copyright belongs to the original author all editors: Zhang Runxin article from Wechat official account: Origin Reading (ID:tupydread), author: Wei Fengwen, Wu Yi, Editor: Zhang Runxin

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