*(Diagram of a solenoid and its magnetic field lines. The shape of all lines was computed according to the laws of electrodynamics. )*

**Electromagnetism** is the branch of physics that studies the interactions between electrically charged particles, whether at rest or in motion, and more generally the effects of electricity, using the notion of electromagnetic field. It is also possible to define electromagnetism as the study of the electromagnetic field and its interaction with charged particles.

Electromagnetism is, with mechanics, one of the great branches of physics whose field of application is considerable. In addition to electricity, electromagnetism makes it possible to understand the existence of electromagnetic waves, that is to say radio waves as well as light, or even microwaves and gamma radiation. Thus, in his 1864 article, *A Dynamical Theory of the Electromagnetic Field*, Maxwell wrote: “The agreement of the results seems to show that light and magnetism are affections of the same substance, and that light is an electromagnetic disturbance propagated through the field according to electromagnetic laws.”

From this point of view, the whole optics can be seen as an application of electromagnetism. Electromagnetic interaction, a strong force, is also one of the four fundamental interactions; it makes it possible to understand (with quantum mechanics) the existence, cohesion and stability of chemical buildings such as atoms or molecules, from the simplest to the most complex.

From the point of view of fundamental physics, the theoretical development of classical electromagnetism is at the source of the theory of special relativity at the beginning of the twentieth century. The need to reconcile electromagnetic theory and quantum mechanics led to the construction of quantum electrodynamics, which interprets the electromagnetic interaction as an exchange of particles called photons. In particle physics, the electromagnetic interaction and the “weak interaction” are unified in the framework of electroweak theory.

#### Concepts

The so-called classical electromagnetism corresponds to the “usual” theory of electromagnetism, developed from the work of Maxwell and Faraday. This is a classical theory because it is based on continuous fields, as opposed to quantum theory. On the other hand, it is not a non-relativistic theory: indeed, although previously proposed to the theory of restricted relativity, Maxwell’s equations, which are at the base of the classical theory, are *invariant* by Lorentz transformation.

The fundamental concept of the theory is the notion of electromagnetic field, an entity which includes the electric field and the magnetic field, which is reduced in some particular cases:

- The charges are immobile: one is then in
*electrostatic*, with static electric fields. - The charge density is zero and the currents are constant in time: one is in
*magnetostatic*, with a static magnetic field. - When the currents are relatively weak, are variable and move in isolated conductors – electrical wires -, the magnetic fields produced are very localized, in elements called self-inductance coils, transformers or generators, with the non-zero electrical charge densities in capacitors or current generating batteries: we are then in
*electrokinetics*; weak currents (electronics) and strong currents (electrotechnics) are distinguished. There is no field outside the circuit (or residual “a bit” depending on the design). We study electrical circuits, and we distinguish between low frequencies and high frequencies. Electronics has made tremendous progress from the development of semiconductors, which are now used to make increasingly miniaturized integrated circuits, and incorporating electronic chips or microprocessors. - The high frequencies, reached by the electric resonant circuits, made it possible, by means of antennas, to create electromagnetic waves, thus eliminating the wires of connection. The emission, propagation and reception of these waves, which are governed by Maxwell’s equations, constitute
*electromagnetism*.

The electromagnetic interaction, presented in fundamental terms of theoretical physics, is called *electrodynamics*; if we take into account the quantum aspect, it is relativistic *quantum electrodynamics*.

This formalism is similar to that of quantum mechanics: the resolution of the Schrödinger equation, or its relativistic version (the Dirac equation), gives the probability of presence of the electron, and the solution of the Maxwell equation, long interpreted as a wave, is basically a probability equation for the photon, which has neither charge nor mass, and moves only at the speed of light in a vacuum.

##### Fundamental interactions

The electromagnetic interaction is one of the four known fundamental interactions. The other fundamental interactions are:

- The weak nuclear interaction, which binds to all known particles in the standard model, and causes some forms of radioactive decay. However, in particle physics, the electroweak interaction is the unified description of two of the four known fundamental interactions of nature: electromagnetism and weak interaction;
- The strong nuclear interaction, which binds quarks to form nucleons, and binds the nucleons to form nuclei;
- The gravitational interaction.

If the electromagnetic force is involved in all forms of chemical phenomena, the electromagnetic interaction is the responsible thing for practically all the phenomena that one encounters in everyday life above the nuclear scale, with the exception of gravity. Roughly speaking, all the forces involved in the interactions between atoms can be explained by electromagnetic forces acting between the electrically charged atomic nuclei and the electrons of the atoms. The electromagnetic force also explains from their movement how these particles have a movement. This includes ordinary forces to “push” or “pull” ordinary material objects. They result from the intermolecular forces that act between the individual molecules of our body and those of objects.

A necessary part for the understanding of the intra-atomic and intermolecular forces is the effective force generated by the electrons, by the momentum of their motion, so that when the electrons move between interacting atoms, they exert a motion with them. As the collection of electrons becomes more confined, their minimum impulse necessarily increases because of the Pauli exclusion principle. The behavior of the material at the molecular scale, including its density, is determined by the equilibrium between the electromagnetic force and the force generated by the momentum exchange carried by the electrons themselves.

#### Electromagnetic field and sources

The theory links two categories of fields and fields linked together, whose expressions are related to the (Galilean) study repository, each field generally depending on time:

- The electromagnetic field, constituted by the data of two vector fields, the electric field
**E**=**E**(r,t), which is expressed in volts per meter (Vm^{-1}), and the magnetic field**B**=**B**(r,t), which is expressed in teslas (T). The concept of the electromagnetic field was coined in the 19th century to uniquely describe electrical and magnetic phenomena. Phenomena such as induction show, indeed, that the electric and magnetic fields are linked together, even in the absence of sources:- A variable magnetic field
**B**generates an electric field; - A variable electric field
**E**is a source of a magnetic field.

This coupling effect between the two fields does not exist in electrostatic and magnetostatic, which are two branches of electromagnetism studying the effects respectively of fixed electrical charges and permanent electric currents.

- A variable magnetic field
- The sources of the electromagnetic field, most often modeled by a scalar field called density charge
**ρ**=**ρ**(r,t), and a vector field called volume density of current**j**=**j**(r,t). This notion of “source” does not necessarily mean that a presence is indispensable for the existence of an electromagnetic field: it can actually exist and propagate in a vacuum.

##### Special case of the static regime

In static mode, when the load and current distributions are time-independent, the electric and magnetic fields are directly related, respectively, to the charge and current densities:

- A fixed charge distribution generates a static electric field, called an electrostatic field, whose expression is directly related to the geometry of the charge distribution;
- A distribution of permanent currents generates a static magnetic field, called the magnetostatic field, whose expression is, again, directly related to the geometry of the current distribution.

This static direct link between the electric and magnetic fields, on the one hand, and the load and current distributions, on the other hand, means that the static fields are not independent dynamic variables. On the other hand, in variable mode, the coupling between the two fields is the source of a complex dynamic (delay, propagation, …), which conceptually raises the electromagnetic field to the rank of a real physical system, endowed with an energy, impulse and kinetic moment, as well as its own dynamics.

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