four equations that explain electromagnetism
Can you imagine how difficult this can be? combine an entire scientific discipline in a few simple equations? And for this there is not only the problem of obtaining elegant equations which summarize hundreds of centuries of knowledge and a very wide field of research, but require a perfect understanding of all the details of this branch of science and excellent mastery of mathematics.
Well, in the 19th century this task was conceived by a brilliant mind James Clerk Maxwell, Scottish physicist whose work laid the foundation for a revolution in the understanding of the fundamental forces of nature. The main discipline is electromagnetismmodeling the behavior of the Earth’s magnetic and electric fields, and which Maxwell managed to tame using the approach consistent theory and four elegant equations.
FROM AMPERE TO GAUSS
Maxwell’s monumental achievement in unifying the forces of electromagnetism was the culmination of the work of many scientists who contributed to the study of this discipline through various observations and theories. For example, in the 1790s, the French physicist Ampere had already formulated first mathematical laws describing the interaction of electric currents and magnetic fields. It was his experiments with electrical conductors and currents that laid a solid foundation for understanding attitude between electricity and magnetism.
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Michael Faraday twenty years later made fundamental discoveries in the field of electromagnetic induction, demonstrating that a magnetic field that was not constant could generate an electric current. However, despite these achievements, the theory of electromagnetism was theoretically incomplete: Faraday’s law coexisted with Ampere’s law, but failed to integrate fully. As if this were not enough, the available equations were specific to certain cases, but had shortcomings when applied to more general cases.
CHALLENGE OF ASSOCIATION
Thus, the development of communication and electrical technologies emphasized the need for a theory that could explain all electromagnetic phenomena. coexisting And fully integrated. Several physicists recognized this problem and made very important contributions that later raided way for Maxwell. Among them, Hermann Helmholtz, who formulated the law of conservation of energy, and William Thomson, who deeply studied the theory of the ether and lines of force, stood out.
However, it was Maxwell who took upon himself the task of carefully and scrupulously studying existing equations and using the ideas of these scientists to unify the laws of electromagnetism into four equations, thereby condensing the entire discipline into simple mathematical formulas applicable to both general cases and more specific situations.
To do this, Maxwell realized that Ampere’s and Faraday’s laws were actually two aspects of a broader phenomenon: by introducing the concept of electric and magnetic fields that vary with time, and formulating the resulting equations, Maxwell obtained a unified theory that: by explaining known phenomena, succeeded in predicting the existence of electromagnetic wavesincluding the light.
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FOUR EQUATIONS
So what were these four equations that Maxwell used to connect electricity and magnetism? The first of these is known as Gauss’s law for electric fieldand expresses in general terms the way in which electric charges can generate electric fields. That is, it is a way of expressing how electric charge It interacts with its environment by creating electric fields.
Secondly, Maxwell stipulated the challenge Gauss’s law for magnetic field, which describes how it is impossible for magnetic monopoles to exist and that the lines forming a magnetic field must always be closed. In other words, a magnetic object must always have north pole and one south: It is impossible to find a magnet with only one pole.
The third law is known as Faraday’s law of electromagnetic induction.. With it, Maxwell explains that whenever there is a moving magnetic field, a magnetic field will be induced. electromotive force, that is, a kind of electric spark. It’s as if somehow the magnetic movement generates electricity.
Cover of the first volume of the first edition of Maxwell’s Treatise on Electricity and Magnetism.
Finally, in the fourth equation, Maxwell brings us to the collision of electric and magnetic fields. This Ampere-Maxwell law and directly connects the circulation of the electric field along a closed curve with rate of change magnetic field over time.
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INFLUENCE
Collectively they are known as Maxwell’s equations and form the basis of all electromagnetic theory. The elegance and versatility of the equations have made it possible to explain a wide range of electromagnetic phenomena, as well as to facilitate technological developments that turned aroundcompletely, modern society.
Collectively they represent a triumph. In this way, they not only revolutionize physics, but also expand their influence. from wireless communications to power generation and medical technologydemonstrating how a deep understanding of electromagnetism and its unification allowed different cases to be considered within the same theory, leading to innovations that completely changed the world as we know it.