Maxwell's equations

The “Maxwell's equations” are a set of four equations (which can be written in both differential and integral form) formulated by the famous mathematician and physicist James Clerk Maxwell, whose country is England. Such equations make up the pillars of classical electromagnetic theory (and variants), and this is what enables us today to use essential equipment for our daily lives, such as light bulbs, navigation, radio and, therefore, even the internet. Given the magnitude of the importance of electromagnetic theory, it is not difficult to imagine that its development was not spontaneous, rather it came along with the evolution of humanity itself. It is also relevant to highlight that electromagnetism is essentially the correlation between magnetic and electrical phenomena.

Ancient people already had contact with electricity and magnetism by merely observing events such as, in the case of electricity, thunder (lightning from thunderstorms) and the famous "shocks" (as when suddenly a person touching something or someone gets an electrostatic shock). This "naive" view of such phenomena continued until the mid-nineteenth century, and human understanding of them was only qualitative.

However, in the 1780s Charles Augustin de Coulomb, known only as Coulomb, defined Coulomb's law, which made it possible to define the rules of electrostatic charges (that is, without movement). Coulomb's law (equation 1) resembles, in a certain way, Newton's universal gravitation (equation 2).

Subsequently, André-Marie Ampère, known as Ampère, conducted experiments which promoted a great advance in our understanding of electromagnetism. Ampère realized that, given a strong enough electric current (flow / motion of charged particles), a magnetized compass needle would orientate perpendicular to the direction of the current, thus establishing a strong relationship between magnetism and the electricity.

Following the chain of contributing scientists comes the brilliant Michael Faraday, whose essence was marked by curiosity. Faraday attended school only until he was 13, afterwards he had to work to help his family. However, Faraday was later "discovered" by Humphry Davy, who made the young man his laboratory assistant. However, Michael Faraday's relative lack of education did not prevent the scientist from making various contributions to science, having his name incorporated with the greatest minds in history. Faraday, through careful observation, creativity and commitment, succeeded in creating the world's first electric motor (the contemporary world has an unthinkable debt to Faraday!). Moreover, the physicist experimentally found that the change (not mere presence) in a magnetic field causes the induction of an electric current (the other way round is also valid, as verified by experiments).

Despite making numerous contributions to physics, Faraday (and no other scientist to date) had managed to quantitatively systematize the ideas of electricity and magnetism. It was then that Maxwell obtained a mathematical correlation of the phenomena, giving rise to the formal classical electromagnetism, today based on the four “lean” equations, namely: “Gauss's law” (equation 3), “Gauss's law for magnetism” ( equation 4), “Faraday's law” (equation 5) and “Ampere's law with Maxwell's correction” (equation 6).

Today we have derivations of classical electromagnetism, such as the most complete “quantum electrodynamics” (QED) and relativistic formulations. It is factual that electromagnetic theory is one of the most important achievements science has ever accomplished, enabling us to enjoy many indispensable resources today, such as electrical appliances, overall technology, and essentially electricity.

Photos: equations(numbered in text) and James Clerk Maxwell

Sources: https://engagedscholarship.csuohio.edu/cgi/viewcontent.cgi…& Física experimental (Cristiane R. C. Tavolaro)