Electromagnetic theory basic equations

OPTICAL EFFECTS OF AN EXTENDED ELECTROMAGNETIC THEORY 29 The basic equations then reduce to... 

Traditionally, physics emphasizes the local properties. Indeed, many of its branches are based on partial differential equations, as happens, for instance, with continuum mechanics, field theory, or electromagnetism. In these cases, the corresponding basic equations are constructed by viewing the world locally, since these equations consist in relations between space (and time) derivatives of the coordinates. In consonance, most experiments make measurements in small, simply connected space regions and refer therefore also to local properties. (There are some exceptions the Aharonov-Bohm effect is an interesting example.)... 

In electromagnetic theory it is shown that the real and imaginary part of e (co) are not independent of each other, but are connected by a pair of integral equations, the Kramers-Kronig relation (e.g. Bohren Huffman 1983). Equation (A3.10) satisfies these relations, i.e. using a Lorentz-Drude model fitted to the laboratory data automatically guarantees that the optical data satisfy this basic physical requirement. 

The SI equations of electromagnetic theory are usually used with physical quantities in SI units, in particular the four units m, kg, s, and A for length, mass, time and electric current. The basic equations for the electrostatic force between charges Qx and Q2, and for the electromagnetic force between current elements It dlx and I2 d/2, in vacuum, are written... 

In this Chapter I will introduce the basic equations governing the electromagnetic field in inhomogeneous conductive media, and review the basic physical laws important in developing electromagnetic inverse theory. 

In order to understand the optical properties of materials, it may be useful to review some basic electromagnetic theory that governs the interaction of electromagnetic waves with matter. We will start with Maxwell s equations. 

The present theory has been developed in terms of an extended Lorentz invariant form of the electromagnetic field equations, in combination with an addendum of necessary basic quantum conditions. From the results of such a simplified approach, theoretical models have been obtained for a number of physical systems. These models could thus provide some hints and first... 

In a strict sense, the classical Newtonian mechanics and the Maxwell s theory of electromagnetism are not compatible. The M-M-type experiments refuted the geometric optics completed by classical mechanics. In classical mechanics the inertial system was a basic concept, and the equation of motion must be invariant to the Galilean transformation Eq. (1). After the M-M experiments, Eq. (1) and so any equations of motion became invalid. Einstein realized that only the Maxwell equations are invariant for the Lorentz transformation. Therefore he believed that they are the authentic equations of motion, and so he created new concepts for the space, time, inertia, and so on. Within... 

This picture is developed to a high level of sophistication within the classical theory of the electromagnetic field, where dynamics is described by the Maxwell equations. Some basics of this theory are described in Appendix 3 A. Here we briefly outline some of the important results of this theory that are needed to understand the nature of the interaction between a radiation field and a molecular system. 

In order to understand how light ean be controlled, we must first review some of the basic properties of the electromagnetic field [8], The eleetromagnetic theory of light is governed by the equations of James Clerk Maxwell. The field phenomena in free space with no sources are described by the basic set of relationships below ... 

Motion, stress, energy, entropy, and electromagnetism are the concepts upon which field theories are constructed. Laws of conservation or balance are laid down as relating these quantities in all cases. These basic principles, which are in integral form, in regions where the variables change sufficiently smoothly are equivalent to differential field equations at surfaces of discontinuity, to jump conditions. 

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