How did Maxwell discover the theory of electromagnetic field?

183 1 year 1 month 65438+3 years, just after Faraday discovered electromagnetic induction, Maxwell was born in Edinburgh, the capital of Scotland. Unlike Faraday, who was born in poverty, his family is knowledgeable and there are many famous scholars in his ancestors. Father has a property in the country: he is a lawyer by profession, but his interest is science and technology. He likes designing machines, science and asking questions. Maxwell was influenced since he was a child, and he was outstanding in middle school. The following year he was admitted to the University of Edinburgh. Three years later, he transferred to Cambridge University and graduated with the second place in first-class mathematics. Influenced by his father, Maxwell was interested in practical problems. His research topic is how to use mathematics to solve physical, astronomical or engineering problems.

After graduating from Cambridge University, Maxwell first studied the color theory of light. Soon he read Faraday's electromagnetic experimental research. Newton's vacuum is replaced by a field full of force lines, and Newton's function in the distance is replaced by a force field in the form of waves and finite velocity. This extraordinary bold insight inspired Maxwell's imagination and resonated with him. But Maxwell also saw that Faraday's expression method was not rigorous enough and there were loopholes. It is here that he can give full play to his talents in mathematics.

Maxwell's first sentence in the electromagnetic paper "On Faraday's magnetic field lines" is: "The current situation is particularly unfavorable for thinking about the science of electricity." Maxwell wanted to improve this situation. He used Faraday's idea of magnetic field lines to clearly show mathematicians and physicists the internal relations between various completely different phenomena discovered by Faraday. To do this, two conditions must be met: ① to define the physical concept and establish an analogy physical model; ② Accurate quantitative relations should be given with mathematical tools. Faraday's physical description of the magnetic field lines around the current is summarized by Maxwell as a vector differential equation. This is a good start, Faraday's physical intuition and Maxwell's mathematical analysis skills began to meet.

Faraday is 40 years older than Maxwell. Their origins, education, personalities and hobbies are quite different. One is from the bottom of society, and the other is an aristocrat. One didn't even graduate from primary school, and the other was high flyers from a famous university. Faraday's speech is beautiful and fascinating; Maxwell is quick-witted and sharp-tongued, but he just plays it by himself, whether the listener understands it or not. One is a master of experiments, and the other is a master of mathematics. One is good at using intuition, grasping the essence of physical phenomena, and designing ingenious experiments, observations, records and induction; One is good at establishing physical models and using mathematical skills to deduce, analyze and improve them. If we combine their characteristics, they will be an ideal physicist. Now they have come together. They firmly believe in the materiality of the field and oppose Newton's action at a distance; Their goal is the same-to establish a brand-new electromagnetic theory that is not subordinate to Newton's natural philosophy system.

Before Maxwell established his electromagnetic theory, German physicists Neumann and Weber inherited Ampere's viewpoint of action at a distance, made many contributions to electromagnetic phenomena's research, and formed the so-called continental school of electrodynamics. However, they tried to understand electromagnetic phenomena within the framework of mechanics, and put forward various complex interaction "potentials" to describe the electromagnetic process. The theory is complicated and unnatural, and a unified theoretical system has not been established. Maxwell, on the other hand, inherited Faraday's concept of proximity and made decisive progress.

Maxwell established the electromagnetic theory in three steps, which lasted 10 years. He focused on Faraday's magnetic field lines from the beginning.

1856, he published the first paper on electromagnetic theory, about Faraday's magnetic field lines. On the basis of Kelvin's analogy research on heat conduction, fluid motion and electric magnetic field lines, it is the first time to try to express Faraday's concept of magnetic field lines as an accurate mathematical form. In this article, he gives the differential relation of the known law of electric field.

1862 published the second paper "On the Force Line of Physics". In this paper, he proposed a molecular eddy current ether model, and all the known basic laws in electricity and magnetism can be obtained by mathematical calculation. In addition, Maxwell introduced the concept of "displacement current" on the basis of this model: changing the electric field causes the change of the electric displacement of the medium, thus exciting the magnetic field in the surrounding space like conducting current. The displacement current is entirely Maxwell's original creation (without any experimental suggestion, it is boldly introduced to ensure the self-consistency of the theory-compatible with the law of conservation of charge). So Maxwell's electromagnetic theory is not only the mathematical accuracy of Faraday's thought. It is pointed out that the displacement current not only ensures the self-consistency of the theory, but also makes the theory have a relativity: the changing electric field excites the vortex magnetic field in the surrounding space, and the changing magnetic field excites the vortex electric field in the surrounding space, which provides a basis for the independent existence of alternating electric field and magnetic field-electromagnetic field separated from the field source. Electromagnetic field is a new type of motion, which propagates in space in the form of shear waves, forming so-called electromagnetic waves.

1865 published the third paper "electromagnetic field dynamics theory". He did not use the ether model he proposed in the past, but summed up Maxwell's equations, the basic equations of electromagnetic field named after him, through mathematical analysis. From this set of equations, he deduced the wave equation satisfied by electromagnetic field and predicted the existence of electromagnetic wave. Because the calculated propagation speed of electromagnetic wave in vacuum is the same as the speed of light in vacuum, Maxwell asserted that light is an electromagnetic wave with a certain frequency and established the electromagnetic theory of light. This is the result of combining theory with experiment.

Maxwell's solid mathematical foundation laid the foundation for his success. Mathematics is extremely important as a tool for physical research. There is no doubt that Maxwell could not get Maxwell's relation without a solid mathematical foundation and strict logical thinking ability. It should also be noted that Maxwell first deduced new equations from the model, and then dared to abandon the original mechanical analogy, so that the electromagnetic field theory was freed from the mechanistic framework and became an independent object. This is the greatness of Maxwell. Someone once said such a metaphor: for Maxwell, when building a tall building, the mechanical model is like a scaffold. After the building was built, the scaffolding was removed bit by bit. This is in sharp contrast to the ampere mentioned earlier. He was completely imprisoned by his own theoretical framework, thus losing the opportunity to discover electromagnetic induction. This is actually a typical example of the important role of innovative thinking in the process of scientific development, which has certain enlightenment for us to cultivate innovative thinking consciousness in the process of teaching and learning today.

Maxwell's equations are listed as one of "10 formulas to change the world". When Faraday and Maxwell built the electromagnetics building, an outstanding physicist-Hertz appeared. He confirmed the existence of electromagnetic waves through experiments. Less than six years later, Italian Marconi and Russian popov realized long-distance radio transmission respectively. The rapid development of wireless telegraph, radio broadcasting, wireless telephone, television, radar and countless radio technologies has made human life unprecedentedly colorful.