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# 物理代写|电动力学代考Electrodynamics代写|PHYS613 Implicit definition of the vectors: polarization, electric induction

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## 物理代写|电动力学代考Electrodynamics代写|Implicit definition of the vectors: polarization, electric induction

Up to this moment we have considered matter only as a set of charged point particles and electromagnetic field, implemented in vacuum. Now we intend to go to a description, typical for physics, of continuum: the charged particles and the field will be described on a base of densities: the density of charge and density of current together with the electromagnetic field defined for each point of space. We however suppose that in a vicinity of such point there is a domain for which one could neglect a change of number of points and correspondent inhomogeneities of electromagnetic field due to smallness of the points itself as sources of the field. Such logic mainly relies upon either an empiric introduction of the field in continuum or on the statistical physics approach. Statistical physics starts from the distribution function as probability density in phase space—state space of classical particles—and, in such way, also introduces fields of continuous media—by means of a procedure of
averaging evaluation in velocity subspace eliminating so far too detailed a description. This description should take into account the quantum nature of microscopic particles and fields. We however, in standard conventional didactics (electrodynamics traditionally go ahead of quantum and statistical mechanics) cannot base neither on statistical physics nor quantum mechanics, hence we shall ‘combine’ possibilities of empiric approach. It is useful to understand the academic tradition.

## 物理代写|电动力学代考Electrodynamics代写|On implicit definition of magnetization vector and magnetic field strength

In an external electromagnetic field the electrons under action of the Lorentz force are moving both translationally and rotationally. hence each matter unit (either atom or molecule) represents a microscopic electric contour. Such contour have a magnetic moment (see equation (3.142)), which at the macroscopic level induces correspondent division of the current density, i.e. the vector $\vec{j}$.

So, in a polarizing matter, the electric current density $\vec{j}$ may be divided to three terms. As the first of them we take the density $\vec{j}{z w}$ related to the matter magnetization, arisen from the electron rotational motion perturbation and spin (apropos, explained by relativistic quantum mechanics), linked to some extra magnetic property, $$\vec{j}{z w}=c \operatorname{rot} \vec{M} .$$
We will use relation (5.6) as the (implicit) definition of a magnetization vector $\vec{M}$.
Another group of terms is related to free current density $j_{s w}$ which represents electrons/ions free motion. The third category is the density of polarization current $\vec{j}{p}$, that arises due to translational motion of coupled charges as variation of electric polarization $$\vec{j}{p}=\frac{d \vec{P}}{d t} .$$

# 电动力学代写

## 物理代写电动力学代考Electrodynamics代写|On implicit definition of magnetization vector and magnetic field strength

$$\vec{j} z w=c \operatorname{rot} \vec{M} .$$

$$\vec{j} p=\frac{d \vec{P}}{d t} .$$

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