By the middle of the 19th century, scientists had discovered a number of laws describing electrical and magnetic phenomena and the connections between them. In particular, the following were known:
 Coulomb’s law, which describes the strength of the interaction between electric charges,
 Gauss’s theorem, which excludes the possibility of the existence of isolated magnetic charges (magnetic monopoles) in nature,
 BiotSavard’s law, which describes magnetic fields excited by moving electric charges (see also Ampere’s Law and Oersted’s Discovery), and
 Faraday’s laws of electromagnetic induction, according to which a change in magnetic flux generates an electric field and induces a current in conductors (see also Lenz’s rule).
These four groups of laws were generalized by James Clerk Maxwell, who managed to combine them into a harmonious system (which received his name), consisting of four equations and comprehensively describing everything measurable characteristics of electromagnetic fields and electric currents, which is named after him. First of all, we owe Maxwell a rigorous mathematical description of all the known laws of electromagnetism (Faraday, for example, generally formulated all the laws he discovered exclusively in verbal form). Secondly, Maxwell introduced many fundamentally new ideas into the system formulated by him, which were absent in the original laws. Third, he gave all electromagnetic phenomena a rigorous theoretical foundation. And finally, fourth, on the basis of the system of equations he compiled, Maxwell made a number of important predictions and discoveries, including the prediction of the existence of a spectrum of electromagnetic radiation.
Let’s start with the second point. According to the BiotSavard law, an electric current passing through a conductor excites a magnetic field around it. What if the electric current does not flow through a conductor, but through a flat capacitor? In fact, electrons do not jump from one plate to another, but the current still passes through the capacitor, since the electrons of one plate interact with the electrons of the other plate, being in close proximity to each other, and, due to mutual repulsion, transmit vibrations to each other (for example called oscillations) alternating current, thereby ensuring the flow of current through a seemingly obvious break in the electrical circuit.
Maxwell realized that Ampere’s law in this situation does not explain the passage of current. He also realized that although charges do not transfer from plate to plate, the electric field (the force that would arise if we placed an imaginary electric charge between the plates) increases. Based on this, he postulated that in the world of electromagnetic phenomena, a changing electric field can play the same role in generating a magnetic field as an electric current. Maxwell introduced a fundamentally new concept bias currentby adding it as a separate term to the generalized Ampere’s law – Maxwell’s first equation. And since then, the presence of displacement currents has been unconditionally confirmed by experimental data.
Having made such an important addition to the first of the four equations, Maxwell, on the basis of the system of equations he compiled, purely mathematically derived a prediction that was fantastic for those times: electromagnetic waves, formed as a result of the vibrational interaction of electric and magnetic fields, and the speed of their propagation should be proportional to the force between charges or between magnets. Having solved his differential wave equation, Maxwell was surprised to find that the speed of propagation of electromagnetic oscillations coincides with the speed of light, which by that time had already been determined experimentally. This meant that a phenomenon so familiar to everyone as light is electromagnetic waves! Moreover, Maxwell predicted the existence of electromagnetic waves in the entire known spectrum – from radio waves to gamma rays. Thus, a thorough theoretical study of the nature of electricity and magnetism led to a discovery that has brought innumerable benefits to mankind – from microwave ovens to Xray units in dental clinics.
1621

Snell’s Law

1864

Spectrum of electromagnetic radiation

1924

Dispersion: atomic theory
