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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|Force Between Two Magnetic Surfaces

In the last section, we determined the energy stored in the magnetic field of a coil. We were able to draw a comparison with the energy stored in a capacitor to predict the energy density in a magnetic field. Now that we are considering the force between magnetic surfaces, can we use the same procedure?

When we considered electrostatic force, we found that the force between two charged plates is given by (Equation (2.55))
$$F=1 / 2 Q E \mathrm{~N}$$
So, we can postulate that the force between two magnetic surfaces is given by
$$F=1 / 2 \phi H \mathrm{~N}$$
The method we will use is the same as the one we used to find the electrostatic force. So, let us consider the arrangement shown in Figure 3.17. This stores a certain amount of energy given by (Equation (3.67))
$$\text { energy }=1 / 2 \mathrm{BH} \mathrm{J} \mathrm{m}^{-3}$$
or
$$\text { energy }=1 / 2 B H \times \text { area } l$$

Now, there will be a force of attraction between the two surfaces. If we move the top surface by a small amount $\mathrm{d} l$, we do work against the attractive force. This work done must equal the change in stored energy. Thus,
\begin{aligned} F \mathrm{~d} l &=1 / 2 B H \times \operatorname{area} \times(l+\mathrm{d} l)-1 / 2 B H \times \text { area } \times l \ &=1 / 2 B H \times \operatorname{area} \times \mathrm{d} l \end{aligned}
Hence,
\begin{aligned} F &=1 / 2 B H \times \text { area } \ &=1 / 2 \phi H \mathrm{~N} \end{aligned}
which agrees with our earlier prediction. The flux and field strength in Equation (3.68) relate to the air gap between the two surfaces. So we can write
$$\text { force }=\frac{1}{2} \frac{B^2}{\mu_0} \times \text { area }$$

## 物理代写|电动力学代写electromagnetism代考|LOW-FreQuency EFfects

At the start of Section 3.10, inductance was introduced as a parameter that limits the current when a coil is connected to an a.c. supply. We saw that a back-emf limits the current with the emf given by (Equation (3.44))
$$e=-L \frac{\mathrm{d} i}{\mathrm{~d} t}$$
where the minus sign shows that the induced emf opposes the supply voltage. An alternative way of looking at this is to say that when a coil is connected to an alternating voltage source, an alternating current flows in the coil. We can find the current by solving the following differential equation
$$v_s(t)=L \frac{\mathrm{d} i}{\mathrm{~d} t}$$
(We should note that the minus sign is missing because Equation (3.70) uses the supply voltage.)

Figure 3.18a shows an inductor connected to an alternating supply. As the source is varying with time, we can write
$$i(t)=I_{\mathrm{pk}} \sin \omega t$$
and so Equation (3.70) becomes
\begin{aligned} v_s(t) &=L I_{\mathrm{pk}} \omega \cos \omega t \ &=L I_{\mathrm{pk}} \omega \sin \left(\omega t+90^{\circ}\right) \end{aligned}
So, when connected to an alternating source, the inductor allows a current to flow with the supply voltage leading the current by $90^{\circ}$. (Figure 3.18b shows the relationship between the supply voltage and the inductor current.)

# 电动力学代考

## 物理代写|电动力学代写electromagnetism代考|Force Between Two Magnetic Surfaces

$$F=1 / 2 Q E \mathrm{~N}$$

$$F=1 / 2 \phi H \mathrm{~N}$$

$$\text { energy }=1 / 2 B H \times \text { area } l$$

$$F \mathrm{~d} l=1 / 2 B H \times \text { area } \times(l+\mathrm{d} l)-1 / 2 B H \times \text { area } \times l \quad=1 / 2 B H \times \text { area } \times \mathrm{d} l$$

$$F=1 / 2 B H \times \text { area } \quad=1 / 2 \phi H \mathrm{~N}$$

$$\text { force }=\frac{1}{2} \frac{B^2}{\mu_0} \times \text { area }$$

## 物理代写|电动力学代写electromagnetism代考|LOW-FreQuency EFfects

$$e=-L \frac{\mathrm{d} i}{\mathrm{~d} t}$$

$$v_s(t)=L \frac{\mathrm{d} i}{\mathrm{~d} t}$$
(我们应该注意，因为公式 (3.70) 使用了电源电压，所以没有减号。)

$$i(t)=I_{\mathrm{pk}} \sin \omega t$$

$$v_s(t)=L I_{\mathrm{pk}} \omega \cos \omega t \quad=L I_{\mathrm{pk}} \omega \sin \left(\omega t+90^{\circ}\right)$$

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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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