Lecture

Electromagnetic Radiation: Exact Solution

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In course

EE-201: Electromagnetics II : field computation

Ce cours traite de l'électromagnétisme dans le vide et dans les milieux continus. A partir des principes fondamentaux de l'électromagnétisme, on établit les méthodes de résolution des équations de Maxwell dans le vide et dans des milieux matériels complexe ...

Description

This lecture covers the exact solution of electromagnetic radiation, including topics such as Maxwell equations, constitutive relations, monochromatic plane waves, free space radiation, vector potential, scalar potential, electromagnetic duality, transmission line theory, Fresnel coefficients, dispersive media, and Lorentz reciprocity. The instructor discusses the fundamental theorems, infinitesimal dipole, uniqueness of the field, and Huygens equivalence principle, providing insights into the behavior of electromagnetic fields in different media.

Instructor

Romain Christophe Rémy Fleury

Official source

Related concepts (32)

Electric potential

The electric potential (also called the electric field potential, potential drop, the electrostatic potential) is defined as the amount of work energy needed per unit of electric charge to move this charge from a reference point to the specific point in an electric field. More precisely, it is the energy per unit charge for a test charge that is so small that the disturbance of the field under consideration is negligible.

Magnetic vector potential

In classical electromagnetism, magnetic vector potential (often called A) is the vector quantity defined so that its curl is equal to the magnetic field: . Together with the electric potential φ, the magnetic vector potential can be used to specify the electric field E as well. Therefore, many equations of electromagnetism can be written either in terms of the fields E and B, or equivalently in terms of the potentials φ and A. In more advanced theories such as quantum mechanics, most equations use potentials rather than fields.

Scalar potential

In mathematical physics, scalar potential, simply stated, describes the situation where the difference in the potential energies of an object in two different positions depends only on the positions, not upon the path taken by the object in traveling from one position to the other. It is a scalar field in three-space: a directionless value (scalar) that depends only on its location. A familiar example is potential energy due to gravity.

Exact solutions in general relativity

In general relativity, an exact solution is a solution of the Einstein field equations whose derivation does not invoke simplifying assumptions, though the starting point for that derivation may be an idealized case like a perfectly spherical shape of matter. Mathematically, finding an exact solution means finding a Lorentzian manifold equipped with tensor fields modeling states of ordinary matter, such as a fluid, or classical non-gravitational fields such as the electromagnetic field.

Electromagnetic four-potential

An electromagnetic four-potential is a relativistic vector function from which the electromagnetic field can be derived. It combines both an electric scalar potential and a magnetic vector potential into a single four-vector. As measured in a given frame of reference, and for a given gauge, the first component of the electromagnetic four-potential is conventionally taken to be the electric scalar potential, and the other three components make up the magnetic vector potential.

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