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

# 物理代写|电动力学代考Electrodynamics代写|FYS2017 Electro- and magneto-statics

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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

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

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

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

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## 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。