Posted on Categories:Electrodynamics, 物理代写, 电动力学

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## 物理代写|电动力学代考Electrodynamics代写|Linear problem

We start directly with the Maxwell system, chapter 10 , section 10.1 .1 , in cylindrical coordinates $\rho, \varphi, z$, see figure 11.3. Bessel functions satisfy orthogonality conditions hence form convenient basis. To complete the statement of the problem, we define the boundary problem with conditions at the point $z=0$ that fix the transversal components (polarizations) of the electric field as a function of time.

The procedure of the projecting is properly described in [45], firstly we expand basic fields in series with respect to the orthogonal waveguide Hondros-Debye basis
$$N_{n l}^{-1} J_l\left(\alpha_{n l} \rho\right) e^{i l p}$$
$N_{n l}$ are the normalization constants for the transverse modes $n l$,
\begin{aligned} E_z(\rho, \varphi, z, t)= & \sum_{l, n} \mathcal{A}{l n}(z, t) J_l\left(\alpha{n l} \rho\right) e^{i l \varphi}+c . c ., \ E_r(\rho, \varphi, z, t)= & \sum_{l, n} \mathcal{B}{l n}(z, t) \frac{i l}{\rho} J_l\left(\alpha{l n} \rho\right) e^{i l \varphi} \ & +\mathcal{C}{l n}(z, t) \frac{\partial}{\partial \rho} J_l\left(\alpha{l n} \rho\right) e^{i l \varphi}+c . c ., \end{aligned}

## 物理代写|电动力学代考Electrodynamics代写|Transformation to frequency domain

Fourier transformation from time to frequency domain provides the solution for the system and leads to the current form
$$\begin{gathered} \frac{\partial}{\partial z} \tilde{\mathcal{A}}{l n}(z, \omega)=-\tilde{\alpha}{l n}^2 \tilde{\mathcal{C}}{l n}(z, \omega), \ \frac{\partial}{\partial z} \tilde{\mathcal{C}}{l n}(z, \omega)=\left(\omega^2 \frac{\varepsilon \mu}{\tilde{\alpha}{l n}^2 c^2}+1\right) \tilde{\mathcal{A}}{l n}(z, \omega), \ \frac{\partial}{\partial z} \tilde{\mathcal{K}}{l n}(z, \omega)=-\tilde{\alpha}{l n}^2 \tilde{\mathcal{M}}{l n}(z, \omega), \ \frac{\partial}{\partial z} \tilde{\mathcal{M}}{l n}(z, \omega)=\left(\frac{\varepsilon \mu}{\tilde{\alpha}{l n}^2 c^2} \omega^2+1\right) \tilde{\mathcal{K}}{l n}(z, \omega) . \end{gathered}$$

This form of the ordinary differential equations with constant coefficients allows us to propose a solution $\tilde{\mathcal{A}}{l n}(z, \omega)=\breve{\mathcal{A}}{l n}(k, \omega) e^{i k z}$, which will be adopted to other variables. Applying this solution to our system, the result
$$\begin{gathered} i k \breve{\mathcal{A}}{l n}(k, \omega)=-\tilde{\alpha}{l n}^2 \breve{\mathcal{C}}{l n}(k, \omega), \ i k \breve{\mathcal{C}}{l n}(k, \omega)=\left(\omega^2 \frac{\varepsilon \mu}{\tilde{\alpha}{l n}^2 c^2}+1\right) \breve{\mathcal{A}}{l n}(k, \omega), \ i k \breve{\mathcal{K}}{l n}(k, \omega)=-\tilde{\alpha}{l n}^2 \breve{\mathcal{M}}{l n}(k, \omega), \ i k \breve{\mathcal{M}}{l n}(k, \omega)=\left(\frac{\varepsilon \mu}{\tilde{\alpha}{l n}^2 c^2} \omega^2+1\right) \breve{\mathcal{K}}{l n}(k, \omega) \end{gathered}$$

# 电动力学代写

## 物理代写|电动力学代考Electrodynamics代写|Linear problem

$$N_{n l}^{-1} J_l\left(\alpha_{n l} \rho\right) e^{i l p}$$
$N_{n l}$ 是横向模式的归一化常数 $n l$,
$$E_z(\rho, \varphi, z, t)=\sum_{l, n} \mathcal{A l n}(z, t) J_l(\alpha n l \rho) e^{i l \varphi}+\text { c.c. }, E_r(\rho, \varphi, z, t)=\quad \sum_{l, n} \mathcal{B l n}(z, t) \frac{i l}{\rho} J_l(\alpha \ln \rho) e^{i l \varphi}+\mathcal{C l n}(z, t) \frac{\partial}{\partial \rho} J_l(\alpha \ln \rho) e^{i l \varphi}+c . c .$$

## 物理代写|电动力学代考Electrodynamics代写|Transformation to frequency domain

$$i k \breve{\mathcal{A}} \ln (k, \omega)=-\tilde{\alpha} \ln ^2 \breve{\mathcal{C}} \ln (k, \omega), i k \breve{C} l n(k, \omega)=\left(\omega^2 \frac{\varepsilon \mu}{\tilde{\alpha} l^2 c^2}+1\right) \breve{\mathcal{A}} \ln (k, \omega), i k \breve{\mathcal{K}} \ln (k, \omega)=-\tilde{\alpha} \ln ^2 \breve{\mathcal{M}} \ln (k, \omega), i k \breve{\mathcal{M}} \ln (k, \omega)=\left(\frac{\varepsilon \mu}{\tilde{\alpha} l n^2 c^2} \omega^2+1\right) \breve{\mathcal{K}} \ln (k, \omega$$

avatest.org 为您提供可靠及专业的论文代写服务以便帮助您完成您学术上的需求，让您重新掌握您的人生。我们将尽力给您提供完美的论文，并且保证质量以及准时交稿。除了承诺的奉献精神，我们的专业写手、研究人员和校对员都经过非常严格的招聘流程。所有写手都必须证明自己的分析和沟通能力以及英文水平，并通过由我们的资深研究人员和校对员组织的面试。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

Posted on Categories:Electrodynamics, 物理代写, 电动力学

## avatest™帮您通过考试

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## 物理代写|电动力学代考Electrodynamics代写|Preparation: Pointing vector for a matter

To define the direction of energy transfer, let us evaluate the averaged in time Pointing vector. The instant flux density in terms of the introduced complex amplitudes $(10.29)$ is proportional to:
$$\mathfrak{E} \times \mathfrak{B}=\frac{1}{4}\left{\mathbf{E} \times \mathbf{B} \exp (2 i \omega t)+\mathbf{E}^* \times \mathbf{B}^* \exp (-2 i \omega t)+\mathbf{E} \times \mathbf{B}^+\mathbf{E}^ \times \mathbf{B}\right}$$

because of the proportionality of the fields $\vec{B}$ and $\vec{H}$, due to equation (10.2). The averaged flux density inside the conducting medium is expressed via Pointing vector:
$$\mathfrak{S}^{\prime \prime}=\frac{c}{4 \pi} \frac{1}{\tau} \int_0^\tau d t \mathfrak{E}^{\prime \prime} \times \mathfrak{B}^{\prime \prime} .$$
Integrals of exponent functions over the time period $\tau=\frac{2 \pi}{\omega}$ give 0 . Hence:
$$\mathfrak{S}=\frac{c}{16 \pi}\left[\mathbf{E} \times \mathbf{B}^+\mathbf{E}^ \times \mathbf{B}\right]$$

## 物理代写|电动力学代考Electrodynamics代写|Polarization choice

Choosing such polarization that the field vector $\mathbf{E}$ lies inside the plane of the vector $\vec{k}$, hence in the two dimensional case via the identity bac-cab, the term of equation $(10.83)$ is rewritten so as
$$-\mathbf{E}_0^{\prime *}\left(\mathbf{E}_0^{\prime \prime}, \overrightarrow{k^{\prime \prime} *}\right)-\mathbf{E}_0^{\prime \prime}\left(\mathbf{E}_0^{\prime \prime *}, \vec{k}^{\prime \prime}\right)$$
into more simple form, adding the opposite terms
$$-\mathbf{E}_0^{\prime \prime *}\left(\mathbf{E}_0^{\prime \prime}, \overrightarrow{k^{\prime \prime}}-2 i \Im \vec{\jmath} \vec{k}^{\prime \prime}\right)-\mathbf{E}_0^{\prime \prime}\left(\mathbf{E}^{\prime \prime *}, \overrightarrow{k^{\prime \prime *}}+2 i \Im \overrightarrow{k^{\prime \prime}}\right)$$

(the symbols $\mathfrak{R}$ and $\mathfrak{I}$ denote real and imaginary parts of a complex number), expanding the expressions we arrive at
\begin{aligned} & -\mathbf{E}_0^{\prime \prime *}\left(\mathbf{E}_0^{\prime \prime}, \overrightarrow{k^{\prime \prime}}\right)-\mathbf{E}_0^{\prime *}\left(\mathbf{E}_0^{\prime \prime},-2 i \Im \overrightarrow{k^{\prime \prime}}\right) \ & -\mathbf{E}_0^{\prime \prime}\left(\mathbf{E}_0^{\prime \prime *}, \overrightarrow{k^{\prime \prime *}}\right)-\mathbf{E}_0^{\prime \prime}\left(\mathbf{E}_0^{\prime *}, 2 i \Im \overrightarrow{k^{\prime \prime}}\right) . \end{aligned}
Now we can apply equations $(10.38),\left(\mathbf{E}_0^{\prime \prime}, \overrightarrow{k^{\prime \prime}}\right)=\left(\mathbf{E}_0^{\prime \prime *}, \overrightarrow{k^{\prime \prime} *}\right)=0$, that result in
$$\mathbf{E}_0^{\prime *}\left(\mathbf{E}_0^{\prime \prime}, 2 i \Im \overrightarrow{k^{\prime \prime}}\right)-\mathbf{E}_0^{\prime \prime}\left(\mathbf{E}_0^{\prime \prime *}, 2 i \Im \overrightarrow{k^{\prime \prime}}\right) .$$

# 电动力学代写

## 物理代写|电动力学代考Electrodynamics代写|Preparation: Pointing vector for a matter

$\backslash$ left 缺少或无法识别的分隔符

$$\mathfrak{S}^{\prime \prime}=\frac{c}{4 \pi} \frac{1}{\tau} \int_0^\tau d t \mathfrak{E}^{\prime \prime} \times \mathfrak{B}^{\prime \prime}$$

$$\mathfrak{S}=\frac{c}{16 \pi}\left[\mathbf{E} \times \mathbf{B}^{+} \mathbf{E}^{\times} \mathbf{B}\right]$$

## 物理代写|电动力学代考Electrodynamics代写|Polarization choice

$$-\mathbf{E}_0^{\prime *}\left(\mathbf{E}_0^{\prime \prime}, \overrightarrow{k^{\prime \prime} *}\right)-\mathbf{E}_0^{\prime \prime}\left(\mathbf{E}_0^{\prime \prime *}, \vec{k}^{\prime \prime}\right)$$

$$-\mathbf{E}_0^{\prime \prime *}\left(\mathbf{E}_0^{\prime \prime}, \overrightarrow{k^{\prime \prime}}-2 i \widetilde{J} \overrightarrow{k^{\prime \prime}}\right)-\mathbf{E}_0^{\prime \prime}\left(\mathbf{E}^{\prime \prime *}, \overrightarrow{k^{\prime \prime *}}+2 i \Im \overrightarrow{k^{\prime \prime}}\right)$$
(符号凡和 $\mathfrak{I}$ 表示复数的实部和虚部)，扩展我们得到的表达式
$$-\mathbf{E}_0^{\prime \prime *}\left(\mathbf{E}_0^{\prime \prime}, \overrightarrow{k^{\prime \prime}}\right)-\mathbf{E}_0^{\prime *}\left(\mathbf{E}_0^{\prime \prime},-2 i \Im \vec{\jmath} k^{\prime \prime}\right) \quad-\mathbf{E}_0^{\prime \prime}\left(\mathbf{E}_0^{\prime \prime *}, \overrightarrow{k^{\prime *}}\right)-\mathbf{E}_0^{\prime \prime}\left(\mathbf{E}_0^{\prime *}, 2 i \vec{\jmath} k^{\prime \prime}\right) .$$

$$\mathbf{E}_0^{\prime *}\left(\mathbf{E}_0^{\prime \prime}, 2 i \Im \overrightarrow{\Im k^{\prime \prime}}\right)-\mathbf{E}_0^{\prime \prime}\left(\mathbf{E}_0^{\prime \prime *}, 2 i \Im \overrightarrow{\jmath k^{\prime \prime}}\right)$$

avatest.org 为您提供可靠及专业的论文代写服务以便帮助您完成您学术上的需求，让您重新掌握您的人生。我们将尽力给您提供完美的论文，并且保证质量以及准时交稿。除了承诺的奉献精神，我们的专业写手、研究人员和校对员都经过非常严格的招聘流程。所有写手都必须证明自己的分析和沟通能力以及英文水平，并通过由我们的资深研究人员和校对员组织的面试。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

Posted on Categories:Electrodynamics, 物理代写, 电动力学

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## 物理代写|电动力学代考Electrodynamics代写|Wire DW model

The exact solutions of equation (9.42) are found in [9], we take the simplest one, corresponding to the ‘planar’ DW model.
$$\Omega(\vec{r}, t)=\Sigma(\vec{r})-\frac{i \gamma}{1-i \alpha} H t,$$
where, the function $\Sigma(\vec{r})$ can be written in the following form:
$$\Sigma=\beta^{\prime} z+\rho[A \cos (\nu \varphi)+B \sin (\nu \varphi)],$$
where $\beta^{\prime}$, is real, $A=A^{\prime}+i A^{\prime \prime}, B=i B^{\prime \prime}$ and $A^{\prime}, A^{\prime \prime}, B^{\prime \prime}$ are real. In particular, as limitation of boundary condition, we assume the magnetization to be radially directed at points $\varphi=0, \pi / 2, \pi,-\pi / 2[10]$. This condition leads to the following values of parameters: $A^{\prime \prime}=0, B^{\prime \prime}=\pi /(2 R)$, where $R$ is the radius of the inner core of the wire. Hence, the real part of $\Sigma$ simplified as
$$\Sigma=\beta^{\prime} z+\rho\left[A^{\prime} \cos (\varphi)+B^{\prime} \sin (\varphi)\right]$$

## 物理代写|电动力学代考Electrodynamics代写|The stray field of the planar DW

At the wire surface, for the stationary solution, taking $t=0$, without loss of generality, we write
$$\Sigma=\beta^{\prime} z+R A^{\prime} \cos (\varphi),$$
For the real $\Sigma$, equations $(9.43)$ and $(9.50)$ give the projections of the unit magnetization vector
$$\begin{gathered} m^x=\frac{2 \exp \left(\beta^{\prime} z+R A^{\prime} \cos (\varphi)\right)}{1+\exp \left[2 \beta^{\prime} z+R A^{\prime} \cos (\varphi)\right] .}=\frac{1}{\cosh \left[\beta^{\prime} z+R A^{\prime} \cos (\varphi)\right] .}, \ m^y=0, \end{gathered}$$
the form of the hyperbolic cosine in equation (9.51) shows the width of the DW:
$$\Delta=1 / \beta^{\prime} .$$

# 电动力学代写

## 物理代与写|电动力学代䒯Electrodynamics代写|Wire DW model

$$\Omega(\vec{r}, t)=\Sigma(\vec{r})-\frac{i \gamma}{1-i \alpha} H t$$

$$\Sigma=\beta^{\prime} z+\rho[A \cos (\nu \varphi)+B \sin (\nu \varphi)],$$

$$\Sigma=\beta^{\prime} z+\rho\left[A^{\prime} \cos (\varphi)+B^{\prime} \sin (\varphi)\right]$$

## 物理代写|电动力学代考Electrodynamics代写|The stray field of the planar DW

$$\Sigma=\beta^{\prime} z+R A^{\prime} \cos (\varphi),$$

$$m^x=\frac{2 \exp \left(\beta^{\prime} z+R A^{\prime} \cos (\varphi)\right)}{1+\exp \left[2 \beta^{\prime} z+R A^{\prime} \cos (\varphi)\right] .}=\frac{1}{\cosh \left[\beta^{\prime} z+R A^{\prime} \cos (\varphi)\right] .}, m^y=0,$$

$$\Delta=1 / \beta^{\prime} .$$

avatest.org 为您提供可靠及专业的论文代写服务以便帮助您完成您学术上的需求，让您重新掌握您的人生。我们将尽力给您提供完美的论文，并且保证质量以及准时交稿。除了承诺的奉献精神，我们的专业写手、研究人员和校对员都经过非常严格的招聘流程。所有写手都必须证明自己的分析和沟通能力以及英文水平，并通过由我们的资深研究人员和校对员组织的面试。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

Posted on Categories:Electrodynamics, 物理代写, 电动力学

## avatest™帮您通过考试

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## 物理代写|电动力学代考Electrodynamics代写|Electro- and magneto-statics

There are known problems in physics that ignore ‘dynamics’, dependence of the medium and field variables on time. We do not concentrate on such problems because our main direction of investigation is electrodynamics, but mention them, in the context of class of adjacent problems, that may be a limiting case or a basis of the time-dependent fields description. The Maxwell equations for time-independent fields and free charges density $\rho$ and free current density $\overrightarrow{j_{s w}}$ distribution may be split into two groups, the first is used for the electrostatics:
$$\begin{gathered} \nabla \cdot \vec{D}=4 \pi \rho, \ \nabla \times \vec{E}=0 . \end{gathered}$$
While for the magneto-statics we write:
$$\begin{array}{r} \nabla \cdot \vec{B}=0, \ \operatorname{rot} \vec{H}=\frac{4 \pi \vec{j}}{c}, \end{array}$$
It is seen that the first group of equations contains only electric field, while the second one only magnetic field. Such problems are generally formulated for bodies, restricted in space, hence with boundaries. A transition through a boundary needs the formulation of a kind of the fields continuity conditions, based on a solid fundamental relation. It is conventionally the Maxwell’s equations in integral form, i.e. such that is naturally chosen because of the absence of derivatives in its formulations, that are poorly-defined at matter discontinuities, i.e. boundaries.

## 物理代写|电动力学代考Electrodynamics代写|Boundary conditions

If the medium is not continuous at some surfaces, we should use boundary conditions on these borders. One can derive the conditions using equation (9.1), but it is more convenient to use the integral form of Maxwell equations of section 5.1.3. Let us divide the medium to sub-volumes choosing one of them as a principal, denoting it as the $V$ with the corresponding boundary surface. We put for simplicity zero charge and current in a vicinity of a point under consideration $\overrightarrow{r_0}$, so we take the first (Coulomb) one
$$\int_S \vec{D} d \vec{S}=0$$
and apply it to a thin (of small height $h$ ) cylindric volume with the center at $\overrightarrow{r_0}$ as it is shown in the figure 9.1. The integral naturally splits into three ones
$$\int=\int_{S_{\mathrm{w}}}+\int_{S_z}+\int_{S_b}=0,$$
over the internal, external and lateral sides of the cylinder surface. We, as before, suppose that the inhomogeneity scale of the fields $\vec{D}, \ldots$ is much bigger than the cylinder base diameter. We also suppose that the normal unit vector $\vec{n}$ of this closed surface is directed out, as at the figure. Therefore we can write approximately
$$\int_{S_z} \vec{D} d \vec{S}=D_{n z} S, \quad \int_{S_w} \vec{D} d \vec{S}=-D_{n w} S$$

# 电动力学代写

## 物理代写|电动力学代考Electrodynamics代写|Electro- and magneto-statics

$$\nabla \cdot \vec{D}=4 \pi \rho, \nabla \times \vec{E}=0 .$$

$$\nabla \cdot \vec{B}=0, \operatorname{rot} \vec{H}=\frac{4 \pi \vec{j}}{c}$$

## 物理代写|电动力学代考Electrodynamics代写|Boundary conditions

$$\int_S \vec{D} d \vec{S}=0$$

$$\int=\int_{S_{\mathrm{w}}}+\int_{S_z}+\int_{S_b}=0,$$

$$\int_{S_z} \vec{D} d \vec{S}=D_{n z} S, \quad \int_{S_w} \vec{D} d \vec{S}=-D_{n w} S$$

avatest.org 为您提供可靠及专业的论文代写服务以便帮助您完成您学术上的需求，让您重新掌握您的人生。我们将尽力给您提供完美的论文，并且保证质量以及准时交稿。除了承诺的奉献精神，我们的专业写手、研究人员和校对员都经过非常严格的招聘流程。所有写手都必须证明自己的分析和沟通能力以及英文水平，并通过由我们的资深研究人员和校对员组织的面试。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

Posted on Categories:Electrodynamics, 物理代写, 电动力学

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## 物理代写|电动力学代考Electrodynamics代写|Projecting operators approach

In our book we use the projecting operators approach, originating from [22]. That’s a general tool of theoretical physics to split evolution system to a set of equations of the first order in time that naturally includes equations for unidirectional waves or non-wave perturbations corresponding to elementary roots of dispersion equation [23]. It is based on a complete set of projecting operators, each for a dispersion relation root that fixes the corresponding subspace of a linearized fundamental system such as Maxwell’s equations. The method, compared to the one used in [18, $19,26]$, allows us to combine equations of the complex basic system in an algorithmic way with dispersion, dissipation and, after some development, a nonlinearity taken into account and also, introduces combined (hybrid) fields as basic modes. It therefore allows us to formulate effectively a corresponding mathematical problem: initial or boundary conditions in an appropriate physical language in a mathematically correct form.

As part of this method we have a transition to new variables, e.g. of the form
$$\psi^{\pm}=\varepsilon \frac{1}{2} E_i \pm \mu \frac{1}{2} H_j,$$
as did Fleck [18], Kinsler [19, 26] and Amiranashvili [20] in their works. This part is in a sense similar to the projection operator method, use of which we demonstrate here.

## 物理代写|电动力学代考Electrodynamics代写|Projecting operators construction

We begin with the system of equations (8.24), using the transformations (8.13) and $(8.14)$
\begin{aligned} & \frac{\varepsilon_0}{\sqrt{2 \pi}} \frac{\partial}{\partial t}\left(\int_{-\infty}^{\infty} \varepsilon(\omega) \mathcal{E}(x, \omega) \exp (i \omega t) d \omega\right) \ & =-\frac{1}{\mu_0 \sqrt{2 \pi}} \frac{\partial}{\partial x}\left(\int_{-\infty}^{\infty} \frac{\mathcal{B}(x, \omega)}{\mu(\omega)} \exp (i \omega t) d \omega\right) . \end{aligned}
Its inverse Fourier transformation origin of the first equation of (8.24) looks as
$$\frac{\partial \mathcal{B}}{\partial x}=-i \omega \mu_0 \varepsilon_0 \mu(\omega) \varepsilon(\omega) \mathcal{E} .$$

Similarly, Fourier transform of the Faraday equation (8.4) gives:
$$\frac{\partial \mathcal{E}}{\partial x}=-i \omega \mathcal{B} .$$
By definition $c^2=\frac{1}{\varepsilon_0 \mu_0}$, where $c$ is the velocity of light in vacuum. Put the notation:
$$\mu_0 \varepsilon_0 \varepsilon(\omega) \mu(\omega) \equiv c^{-2} \varepsilon(\omega) \mu(\omega) \equiv a^2(\omega) .$$
The system (8.28) and (8.29) simplifies as:
$$\begin{gathered} \frac{\partial \mathcal{B}}{\partial x}=-i \omega a^2(\omega) \mathcal{E} \ \frac{\partial \mathcal{E}}{\partial x}=-i \omega \mathcal{B} \end{gathered}$$

# 电动力学代写

## 物理代写|电动力学代考Electrodynamics代写|Projecting operators approach

$$\psi^{\pm}=\varepsilon \frac{1}{2} E_i \pm \mu \frac{1}{2} H_j,$$
Fleck [18]、Kinsler [19、26] 和 Amiranashvili [20] 在他们的作品中也是如此。这部分在某种意义上类似于 我们在这里演示的投影算子方法。

## 物理代写|电动力学代考Electrodynamics代写|Projecting operators construction

$$\frac{\varepsilon_0}{\sqrt{2 \pi}} \frac{\partial}{\partial t}\left(\int_{-\infty}^{\infty} \varepsilon(\omega) \mathcal{E}(x, \omega) \exp (i \omega t) d \omega\right) \quad=-\frac{1}{\mu_0 \sqrt{2 \pi}} \frac{\partial}{\partial x}\left(\int_{-\infty}^{\infty} \frac{\mathcal{B}(x, \omega)}{\mu(\omega)} \exp (i \omega t) d \omega\right) .$$
(8.24)式第一个方程的傅里叶逆变换原点为
$$\frac{\partial \mathcal{B}}{\partial x}=-i \omega \mu_0 \varepsilon_0 \mu(\omega) \varepsilon(\omega) \mathcal{E} .$$

$$\frac{\partial \mathcal{E}}{\partial x}=-i \omega \mathcal{B} .$$

$$\mu_0 \varepsilon_0 \varepsilon(\omega) \mu(\omega) \equiv c^{-2} \varepsilon(\omega) \mu(\omega) \equiv a^2(\omega) .$$

$$\frac{\partial \mathcal{B}}{\partial x}=-i \omega a^2(\omega) \mathcal{E} \frac{\partial \mathcal{E}}{\partial x}=-i \omega \mathcal{B}$$

avatest.org 为您提供可靠及专业的论文代写服务以便帮助您完成您学术上的需求，让您重新掌握您的人生。我们将尽力给您提供完美的论文，并且保证质量以及准时交稿。除了承诺的奉献精神，我们的专业写手、研究人员和校对员都经过非常严格的招聘流程。所有写手都必须证明自己的分析和沟通能力以及英文水平，并通过由我们的资深研究人员和校对员组织的面试。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

Posted on Categories:Electrodynamics, 物理代写, 电动力学

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## 物理代写|电动力学代考Electrodynamics代写|Tokamak plasma

One can create a magnetic field with a solenoid wound around a cylindrical tube, and then roll the tube into a torus to prevent departure of particles along the magnetic field. A D Sakharov and I E Tamm in 1951 proposed a modified scheme formulating a theoretical basis for a thermonuclear reactor where the plasma would have a torus shape and be held by a magnetic field [15].

Such a trap was named a Tokamak, toroidal’naja kamera s magnitnymi katushkami (in Russian) [18]. Its essential element is a torus-mounted formatter that creates a vortex electric field causing a current in the plasma, which heats the plasma.

The plasma description via averaged (hydrodynamic) values of its parameters such as velocity is called magneto-hydro-dynamics (MHD). This complex name simply covers the notion of fluid (hydro) in movement (dynamics) in a magnetic field (magneto), which applies very precisely to what happens inside a tokamak. To confine a hot plasma in an immaterial container formed by the magnetic field lines is a bit like wanting to contain a gas under pressure in a tyre inner tube. See for more details http://physci.llnl.gov/Research/Tokamak/, the spherical alternative is presented in figure 7.3. The general view of the largest international project JET tokamak European Torus, built in England, is given in figure 7.4. The following records certain plasma parameters: temperature 320 million $\mathrm{K}$, concentration $4 \times 10^{20} \mathrm{~m}^{-3}$, energy retention time (see below) $1.8 \mathrm{~s}$. Magnetic field in this setup is almost $4 \mathrm{~T}$, so at a temperature of 100 million $\mathrm{K}$, ions Larmor, the measuring radius is $3.5 \mathrm{~mm}$.

Today (2020) the tokamak-ITER (‘The Way’ in Latin) project reaches its engineering height, being one of the most ambitious projects of energetics in the world to date. It intends to be the heart of the electric plant at the Cadarache facility [16], the ITER Tokamak will be the largest and most powerful fusion device in the world. It should achieve a deuterium-tritium plasma in which the reaction is sustained through internal heating.

## 物理代写|电动力学代考Electrodynamics代写|General remarks on plasma theoretical description

Generally plasma is a rich medium for waves initiation and propagation [26, 27]. As an example of plasma dynamics we choose a description of propagation of helicoidal waves in a model plasma with immobilized positive ions and movable electrons [27]. It is a good example to demonstrate some normal for plasma theory model approximations. The main difference with the previous section is an account of ions dynamics (via momentum balance). Namely such option is a natural step towards a closed matter-field description. We also restrict ourselves by the case of hydrodynamic approximation of the plasma interacting with electromagnetic field. Such description in a frame of small Knudsen numbers $K n=\frac{\nu_w}{\nu} \ll 1$ ( $\nu$ is collisions frequency, $\nu_w$ is a wave frequency), collisions between particles play a basic role, hence plasma may be considered as a conducting fluid. The electrodynamic equations are then in a correspondence with the hydrodynamic level description of particles. Starting with the first Maxwell’s equation (‘Coulomb law’)
$$\operatorname{div} \vec{E}=4 \pi \sum_a e_a n_a,$$
where $e_1=e_{-}$is electron charge and $n_1=n_{-}$denotes electron concentration, the rest indices values mark ions. Here the density of charge in equation (11.16) is written as the sum of ion densities with the charges factors account. Adding the absence of magnetic charges statement
$$\operatorname{div} \vec{B}=0$$
we reproduce Faraday’s law of section 6.1.1.
$$\operatorname{rot} \vec{E}=-\frac{1}{c} \frac{\partial \vec{B}}{\partial t},$$
and close the Maxwell system by the Maxwell-Ampère one
$$\operatorname{rot} \vec{B}=\frac{1}{c} \frac{\partial \vec{E}}{\partial t}+\frac{4 \pi}{c} \sum_a e_a n_a \vec{v}_a$$

# 电动力学代写

## 物理代写|电动力学代考Electrodynamics代奇|关于等离子体理论描述的一般意见

$$\operatorname{div} vec{E}=4 pisum_a e_a n_a,$$

$$\operatorname{div} vec{B}=0$$

$$\operatorname{rot} \vec{E}=-frac{1}{c}。\frac{partial vec{B}}{partial t}。$$

$$\ooperatorname{rot} \vec{B}=frac{1}{c}。\frac{partial vec{E}}{partial t}+frac{4 pi}{c}。\sum_a e_a n_a \vec{v}_a$$

avatest.org 为您提供可靠及专业的论文代写服务以便帮助您完成您学术上的需求，让您重新掌握您的人生。我们将尽力给您提供完美的论文，并且保证质量以及准时交稿。除了承诺的奉献精神，我们的专业写手、研究人员和校对员都经过非常严格的招聘流程。所有写手都必须证明自己的分析和沟通能力以及英文水平，并通过由我们的资深研究人员和校对员组织的面试。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

Posted on Categories:Electrodynamics, 物理代写, 电动力学

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## 物理代写|电动力学代考Electrodynamics代写|Drude theory of metals: Ohm’s law

The Lorentz model for dielectrics may be applied to conductors (metals or, generally for plasma), considering this case as a limit $\omega_0=0$. The result is achieved because of relaxation mechanism is taken into account. The limit may be interpreted as a transition to free electrons of a metal (generally free charges, ions or holes in a solid).
It is considered as a version of the Drude model [12] as a response of a conducting matter to a time-dependent electric field with an angular frequency $\omega$ (cf the DC case in the next section).
An opposite limit $\omega_0 \ll \omega$ may be studied for high frequencies.
The complex amplitude of oscillations in a case of a conductor is given by the formula
$$x_0=\frac{-e E_{0 x}}{m\left(\omega^2+i \gamma \omega\right)} .$$
We will consider relations for the complex amplitudes for the exponential form of solutions.

The polarization vector will hence have the form
$$\vec{P}=\frac{e^2 N}{m} \operatorname{Re}\left[\sum_k \frac{-1}{\omega^2+i \gamma_k \omega}\right] \vec{E},$$
while the dielectric permeability we represent as
$$\begin{gathered} \chi=-\frac{N e^2}{m} \sum_k \operatorname{Re}\left[\frac{1}{\omega^2+i \gamma_k \omega}\right] \ \varepsilon=1-\frac{4 \pi N e^2}{m} \sum_k \operatorname{Re}\left[\frac{1}{\omega^2+i \gamma_k \omega}\right] \end{gathered}$$

## 物理代写|电动力学代考Electrodynamics代写|On the DC Ohm law

The charge transport in the DC case is a nonequilibrium process hence in general theory such a relation as equation (6.79) is derived via the kinetic equation solution with averaging procedure application [5]. In textbooks there often used a simplified theory, that in my imagination can be understood as follows. The quasiparticle which represents the charge transport (say, electron, more precise-polaron) is moving in the phonon (quasiparticle of atom net oscillations) gas of a solid as a drop falling in air. After the start it is accelerated by constant electric field, but soon the acceleration decreases because the electric force is compensated by friction that is proportional to the electron velocity. The equation of motion (of a small sphere) hence is modeled as
$$m \frac{d \vec{v}}{d t}=e \vec{E}-6 \pi \mu R \vec{v},$$
where the second, Stokes drug term is proportional to the radius $R$ and dynamical viscosity $\mu$. The viscosity coefficient in turn is determined by properties of the gas, for example kinetic (Chapman-Enskog) theory for Maxwellian particles gives
$$\mu=n_p k_B T / \lambda,$$
where $n_p$ is the gas concentration, $k_B$-Boltzmann constant, $T$-temperature and the constant $\lambda$-collision integral eigenvalue.

# 电动力学代写

## 物理代写|电动力学代考Electrodynamics代写|Drude theory of metals: 欧姆定律 定律

$$x_0=\frac{-e E_{0 x}}{m\left(\omega^2+i \gamma\omega\right)} 。$$

$$\vec{P}=frac{e^2 N}{m}。\operatorname{Re}\left[\sum_k\frac{-1}{omega^2+i \gamma_k \omega}\right] \vec{E}。$$

$$\chi=-frac{N e^2}{m}。\sum_k operatorname{Re}\left[frac{1}{omega^2+i gamma_komega}\right] varepsilon=1-frac{4pi N e^2}{m}。\sum_k operatorname{Re}\left[\frac{1}{omega^2+i gamma_k`omega}\right] 。$$

## 物理代写|电动力学代考Electrodynamics代写|On the DC Ohm law

$$m\frac{d vec{v}}{d t}=e vec{E}-6 pi mu R vec{v}。$$

$$\黏度=n_p k_B T / \lambda$$

avatest.org 为您提供可靠及专业的论文代写服务以便帮助您完成您学术上的需求，让您重新掌握您的人生。我们将尽力给您提供完美的论文，并且保证质量以及准时交稿。除了承诺的奉献精神，我们的专业写手、研究人员和校对员都经过非常严格的招聘流程。所有写手都必须证明自己的分析和沟通能力以及英文水平，并通过由我们的资深研究人员和校对员组织的面试。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

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## 物理代写|电动力学代考Electrodynamics代写|Magnetics

Bodies with magnetic properties that are such where the magnetization vector $(5.59)$ can be nonzero in some conditions $(\mu \neq 1$, or $\chi \neq 0)$, are named magnetics. Diamagnets were first discovered when Sebald Justinus Brugmans observed in 1778 that bismuth and antimony were repelled by magnetic fields. The term diamagnetism was coined by Michael Faraday in September 1845, when he realized that every material responded (in either a diamagnetic or paramagnetic way) to an applied magnetic field [16].

Its origin is an important problem of modern physics which is considered from a quantum point of view [17]. One of the most important issues on the topic, IEEE Transactions on Magnetics publishes scholarly articles of archival value as well as tutorial expositions and critical reviews of classical subjects and topics of current interest. These are science and technology related to the basic physics and engineering of magnetism, magnetic materials, applied magnetics, magnetic devices, and magnetic data storage.

Classification of matter whose magnetic properties are discussed in connection with problems considered includes wide variety of magnetization vector formulas (5.10) and (5.24), starting from the simplest (5.29)
$$\vec{M}=\chi_m \vec{B}$$
In this case the vector $\vec{M}$ is one, which direction is along the magnetic field acting on a dielectric, where the coefficient $\chi_m$, named the magnetic permeability is obviously linked to $\mu$ via (5.24),
$$\mu=1+4 \pi \chi_m .$$

## 物理代写|电动力学代考Electrodynamics代写|Ferromagnetism

The phenomenon
Let us start with a definition of the ferromagnetic in terms of the equation of state $(\vec{B}(\vec{H})$ dependence). Ferromagnets are conventionally solids (see the previous subsection) in which a dependence between the vectors: magnetic moment $\vec{M}$ and magnetic field $\vec{H}$ is nonlinear and not unique. It means that a growth of the magnetic field stress yields changes in magnetization velocity of a ferromagnetic. So happens till some extremal level is reached, that is named magnetic saturation, $\vec{M} \rightarrow \vec{M}_s$.
The next feature is typical for a ferromagnetic in some temperature range, restricted by Curie temperature: it is a phenomenon of hysteresis. It depends on not only external magnetic field, but also on a level of magnetization of a specimen at $t=0$. Such situation one can present by the plot, so-called hysteresis loop, figure 5.7. Switching on the magnetic field at $(t=0)$, corresponds to the time of magnetization start. In the time marked $t=1$, the hysteresis curve reaches its maximum, saturation point A. Next, switching off the magnetic field, the magnetization of the body diminishes down to the value, corresponding to point B. One can state experimentally that the specimen will have some magnetization, while the external magnetic field is absent. To eliminate the magnetization of the ferromagnetic body, it is necessary to do some actions, applying a magnetic field of the opposite direction, repeating this a few times. The work of such action magnitude is equal to the area of the hysteresis curve marked at the plot.

# 电动力学代写

## 物理代写|电动力学代考|电动力学代写|Magnetics

$$\vec{M}=chi_m\vec{B}$$

$$\δmu=1+4 pi δchi_m 。$$

## 物理代写|电动力学代考|电动力学代写|电磁学现象

avatest.org 为您提供可靠及专业的论文代写服务以便帮助您完成您学术上的需求，让您重新掌握您的人生。我们将尽力给您提供完美的论文，并且保证质量以及准时交稿。除了承诺的奉献精神，我们的专业写手、研究人员和校对员都经过非常严格的招聘流程。所有写手都必须证明自己的分析和沟通能力以及英文水平，并通过由我们的资深研究人员和校对员组织的面试。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

Posted on Categories:Electrodynamics, 物理代写, 电动力学

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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

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

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

avatest.org 为您提供可靠及专业的论文代写服务以便帮助您完成您学术上的需求，让您重新掌握您的人生。我们将尽力给您提供完美的论文，并且保证质量以及准时交稿。除了承诺的奉献精神，我们的专业写手、研究人员和校对员都经过非常严格的招聘流程。所有写手都必须证明自己的分析和沟通能力以及英文水平，并通过由我们的资深研究人员和校对员组织的面试。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

Posted on Categories:Electrodynamics, 物理代写, 电动力学

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## 物理代写|电动力学代考Electrodynamics代写|Relativistic kinematics and four-vectors

The general kinematic idea is arranging all physical variables into such groups, that each of them presents a tensor in Minkowski’s space. Basic coordinates in spacetime $\left(x_{0}=c t, x_{1}=x, x_{2}=y, x_{3}=z\right)$ include the fourth (we call it zero) constituent ct and create the first order tensor – the vector with respect to Lorentz group. For the set of velocity components $v_{i}=\frac{d x_{i}}{d t}$ we naturally add the speed of light $c=\frac{d x_{0}}{d t}$. An important question arises: what is the temporal component $p_{0}$ of the momentum $p_{i}$ ? The sense of this additional component can be explained also by the invariant of a similar combination equation (4.19):
$$m_{0}^{2} c^{2}=p_{0}^{2}-p_{1}^{2}-p_{2}^{2}-p_{3}^{2},$$
marked on the right side with the inclusion, therefore the coefficient $c^{2}$ has been entered. In the rest system $p_{i}=0$, so the zero-component of the quadrupole momentum $p_{0}$ is proportional to the invariant lhs $p_{0}=m_{0} c$. The parameter $m_{0}$ is named as invariant mass.

## 物理代写|电动力学代考Electrodynamics代写|Relativistic mechanics

A fundamental physical postulate is that a transition to a different reference frame should not break the sense of the Maxwell equations. Here, in electrodynamics, let us stress, that the complete set of Maxwell’s equations includes not only field components but, as well, the charge and current density, that, for a charged particle is proportional to its velocity j ⃗= qv⃗. It means that the components of velocity, that enters the mechanics, should transform as the vector components in the space–time[14]. As was mentioned in the previous section 4.3; the fourth component of the fourvector of velocity is the velocity of light. Next, it is important to note that the complete (closed) system of equations (Maxwell ones + Newtons) should include also the Lorentz force [7]. So, we arrive at the main principle of the modern theoretical physics: it is the principle of general covariance [2]. It reads as The basic equations of physics should have the tensor form, each side of equation would have to be a some rank tensor with respect to the Lorentz group.

# 电动力学代写

## 物理代写|电动力学代考Electrodynamics代写|Relativistic kinematics and fourvectors

$\left(x_{0}=c t, x_{1}=x, x_{2}=y, x_{3}=z\right)$ 包括第四个 (我们称之为零) 成分 $\mathrm{ct}$ 并创建一阶张量 – 关于洛伦兹群的向量。对于速度分量 类似的组合方程 (4.19) 的不变量来解释:
$$m_{0}^{2} c^{2}=p_{0}^{2}-p_{1}^{2}-p_{2}^{2}-p_{3}^{2}$$

## 物理代写|电动力学代考Electrodynamics代写|Relativistic mechanics

avatest.org 为您提供可靠及专业的论文代写服务以便帮助您完成您学术上的需求，让您重新掌握您的人生。我们将尽力给您提供完美的论文，并且保证质量以及准时交稿。除了承诺的奉献精神，我们的专业写手、研究人员和校对员都经过非常严格的招聘流程。所有写手都必须证明自己的分析和沟通能力以及英文水平，并通过由我们的资深研究人员和校对员组织的面试。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。