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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 物理代写|电动力学代写electromagnetism代考|Mathematical Approach

In the previous section, we used Gauss’ law to examine the field around an infinitely long charged line. Here, we will split the line into infinitesimally small sections, so that we can use Coulomb’s law as applied to point charges.

Let us consider a small section of the line as shown in Figure 2.12. The charge on this section is $\rho_1 \times \mathrm{d} z$ and so the flux density at point $\mathrm{P}$ is
$$D=\frac{\rho_1 \times \mathrm{d} z}{4 \pi r^2}$$
We should note that this is a vector quantity acting at an angle to the axis of the line. By taking the origin as shown in Figure $2.12$, the line stretches from $-\infty$ to $+\infty$. Thus, we can see that the line is symmetrical about the origin. Now, $\boldsymbol{D}$ can be split into a radial component, $D_r$, and a vertical component, $D_z$, given by
$$D_r=\frac{\rho_1 \times \mathrm{d} z}{4 \pi r^2} \sin \theta r$$
and
$$\boldsymbol{D}z=\frac{\rho{\mathrm{1}} \times d z}{4 \pi r^2} \cos \theta z$$
These flux densities are due to an incremental section of the line. So, to find the total flux density, we can integrate Equations (2.18) and (2.19) with respect to $z$ between the limits of $-\infty$ and $+\infty$. Unfortunately, as we move up and down the line, $r$ and $\theta$ vary as well. If we change variables to integrate with respect to $\theta$, we need to express $z$ and $r$ in terms of $\theta$.

## 物理代写|电动力学代写electromagnetism代考|GAUSs’ LAW APPROACH

Let us consider the circular charged plate shown in Figure $2.13$. This plate has a certain charge spread over its surface. To simplify the analysis, let us assume that the charge distribution is uniform and that there are no edge effects. Now let us consider a small area of the plate. This area will contain a certain amount of charge, $\mathrm{d} Q$, given by
$$\mathrm{d} Q=\rho_s \mathrm{~d} s$$

where $\rho_s$ is the surface charge density in $\mathrm{C} \mathrm{m}{ }^{-2}$, and $\mathrm{d} s$ is the area of the section. Flux emanating from this area will flow upwards and downwards to occupy a cylinder. (There will only be a vertical component of flux because any horizontal flux will cancel out due to symmetry. This is a similar situation to that which we met when we examined line charges.) By applying Gauss’ law, we see that the total flux out of the cylinder, in both directions, must equal the enclosed charge. So, half the flux flows upwards and half flows downwards. Thus, the flux density at any height above the disc is
\begin{aligned} \boldsymbol{D}_z &=\frac{\mathrm{d} Q}{2 \mathrm{~d} s} z \ &=\frac{\rho_s \mathrm{~d} s}{2 \mathrm{~d} s} \boldsymbol{z} \ &=\frac{\rho_s}{2} z \end{aligned}
and the electric field strength is
$$\boldsymbol{E}_z=\frac{\rho_s}{2 \varepsilon_0 \varepsilon_r} z$$
The important thing to note here is that the $\boldsymbol{E}$ field is independent of the distance from the disc. This is a consequence of having the flux flow in a cylindrical tube.

# 电动力学代考

## 物理代写|电动力学代写electromagnetism代考|Mathematical Approach

$$D=\frac{\rho_1 \times \mathrm{d} z}{4 \pi r^2}$$

$$D_r=\frac{\rho_1 \times \mathrm{d} z}{4 \pi r^2} \sin \theta r$$
$\$ \

## 物理代写|电动力学代写electromagnetism代考|GAUSs’ LAW APPROACH

d问=rs ds

D和=d问2 ds和 =rs ds2 ds和 =rs2和

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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。

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