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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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|LINE CHARGES

So far we have only considered point charges. This is very useful when introducing the fundamental laws we have considered. However, we rarely meet point charges in reality. Instead, we come across lines of charge, charged surfaces and charged objects. Thus, we have to deal with charge distributions in one, two and three dimensions.

This is where things tend to get a little complicated, as we have to think in three dimensions. In such cases, it is essential to draw diagrams that help us visualize the situation.

Let us consider a long piece of wire that is charged by some means. Electric flux will radiate outwards from this line of charge and the direction of this flux will be away from the line in a radial direction. If we only consider the central part of the wire, we can ignore what happens at the end of the line and so the flux distribution is as shown in Figure $2.10$.

If we apply Gauss’ law, we can say that the total flux emanating from the wire is equal to the charge enclosed by an imaginary Gaussian surface. In this case, the Gaussian surface will be an open-ended tube with the wire placed along the central axis of the tube (Figure 2.10). To find the flux density, and hence the electric field strength, we can use Gauss’ law or we can use a more rigorous mathematical approach. Both techniques are presented here.

## 物理代写|电动力学代写electromagnetism代考|Gauss’ LaW APProach

Let us consider the line charge and Gaussian surface as shown in Figure $2.10$. The charge is distributed along the length of the wire, and so let us introduce a line charge density given by the total charge, $Q$, divided by the length of the line, $L$, i.e.,
$$\rho_1=\frac{Q}{L}$$
If we consider a unit length of wire $(1 \mathrm{~m})$, we get a total flux of
$$\psi=\rho_1 \times l \mathrm{C}$$
Now, the flux density is the flux divided by the surface area of the Gaussian surface. As the Gaussian surface is a tube, the surface area is the circumference of the tube times the length, i.e.,
$$\text { area }=2 \pi r \times l$$
Thus, the density is
$$\boldsymbol{D}=\frac{\rho_1}{2 \pi r} \boldsymbol{r}$$
and the electric field strength is
$$\boldsymbol{E}=\frac{\rho_1}{2 \pi \varepsilon r} \boldsymbol{r}$$
The equipotential surfaces will be coaxial tubes that have the wire along the centre line of the tubes (Figure 2.11a). So, if we move in a direction parallel to the wire, we do no work against the field indicating that we can ignore travel along the wire. Thus, we can draw a two-dimensional plot as shown in Figure $2.11 \mathrm{~b}$.

# 电动力学代考

## 物理代写|电动力学代写electromagnetism代考|Gauss’ LaW APProach

$$\rho_1=\frac{Q}{L}$$

$$\psi=\rho_1 \times l \mathrm{C}$$

$$\text { area }=2 \pi r \times l$$

$$\boldsymbol{D}=\frac{\rho_1}{2 \pi r} \boldsymbol{r}$$

$$\boldsymbol{E}=\frac{\rho_1}{2 \pi \varepsilon r} \boldsymbol{r}$$

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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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