### 物理代写|电磁学代写electromagnetism代考|PHYSICS 7536

statistics-lab™ 为您的留学生涯保驾护航 在代写电磁学electromagnetism方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写电磁学electromagnetism代写方面经验极为丰富，各种代写电磁学electromagnetism相关的作业也就用不着说。

• 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|电磁学代写electromagnetism代考|Capacitance

We first start with the definition of a capacitor. For that, consider two charged conductors with charges of equal magnitude but of opposite sign, as shown in Fig.4.1. Suppose they are combined, forming a so-called capacitor. The conductors are also called plates. Note that a potential difference $\Delta \phi$ exists between the conductors due to the presence of two different types of charges in each conductor.

Moreover, because the unit of potential difference is the volt, a potential difference is often called a voltage. Here, we denoted it $\Delta V$, which is equal to absolute value of $\Delta \phi, \Delta V \equiv|\Delta \phi|$

The capacity of an electric circuit to accumulate electric charge at a particular value of $\Delta V$ is called the capacity. Based on the experimental results, the amount of charge $Q$ on a capacitor depends linearly on the potential difference $\Delta V$ between the two conductors. Furthermore, the constant of proportionality depends on the shape and distance between the conductors, as in the following demonstrated for a planar capacitor.

We can write this relationship, mathematically, as
$$Q=C \Delta V$$
Here, $Q$ is the amount of charge in each capacitor, that is, $Q=|+Q|=|-Q|$, and hence, $C>0$.

Therefore, the capacitance $C$ of a capacitor (see also Eq. (4.1)) represents the ratio of the magnitude of charge on each of conductors to the magnitude of the potential difference between them:
$$C \equiv \frac{Q}{\Delta V}$$

## 物理代写|电磁学代写electromagnetism代考|Calculating Capacitance

To demonstrate the calculation of the capacitance of a capacitor, we consider a capacitor formed from a pair of parallel plates; each plate is connected to one terminal of a battery acting as a source of potential difference, as shown in Fig. 4.2. Thus, the voltage is $\Delta V$.

We assume that the capacitor is initially uncharged, and the battery establishes an electric field in the connecting wires when the connections are made. The directions of the electric field lines are explained in Fig. $4.2$ (on the left); that is,
$$\phi_{+}-\phi_{A}=-\int_{A}^{(+)} \mathbf{E} \cdot d \mathbf{s}$$
where $d \mathbf{s}$ is a small displacement vector along the left wire, and
$$\phi_{-}-\phi_{B}=-\int_{B}^{(-)} \mathbf{E} \cdot d \mathbf{s}$$
where $d \mathbf{s}$ is a small displacement vector along the right wire. Initially, when $Q=0$ on both plates $\phi_{A}=\phi_{B}=0$, and hence $\mathbf{E} \neq 0$. Therefore, on the plate connected to the negative terminal of the battery, the electric field exerts a force on electrons, which are in the wire just outside this plate; the electrons accelerate to move onto the plate and hence starts charging the plate negatively. On the other hand, the electric field exerts forces on electrons of the side (which is closer to the wire) of the plate

connected to the positive terminal of the battery. It accelerates the electrons to move onto the wire. Hence, leaving on the plate more positive charges in comparison to negative one (electrons); therefore, this plate is charged positively.

Those accelerations continue until the plates, the wires, and the terminals are all at the same electric potential. That is also illustrated in Fig. $4.2$ (on the right). Once the equilibrium point is attained, no potential differences exist between the terminals and the plates on both sides, and hence; as a result, no electric field is present in the wire, $\mathbf{E}=0$, and the movement of electrons stops. The right plate carries a negative charge, $-Q$, and left plate a positive charge, $+Q$. When the equilibrium establishes, the potential difference between the capacitor plates becomes that between the terminals of the battery.

To calculate the capacitance of a pair of oppositely charged conductors by an amount of charge $Q$, we calculate the potential difference $\Delta V$ as
$$\Delta V=\left|\phi_{+}-\phi_{-}\right|$$
Then, the sapacitance is evaluated using the expression given by Ey. (4.2). Note that for simple geometry of the capacitor, these calculations are relatively easy. In the following, we will discuss spherical shape and planar shapes of conductors.

## 物理代写|电磁学代写electromagnetism代考|Spherical Conductors

Let us consider first the capacitance of an isolated spherical conductor of radius $R$ and charge $Q$ concentric with a hollow sphere of infinite radius, which forms the second conductor making up the capacitor. We derived the electric potential of the sphere of radius $R$ as
$$\phi_{R}=k_{e} \frac{Q}{R}$$
Since at infinity $\phi_{\infty}=0$, we obtain
$$C=\frac{\bar{Q}}{\Delta V}=\frac{\overline{k_{e}} Q / R}{}=\frac{\bar{R}}{k_{e}}=4 \pi \epsilon_{0} R$$
where $\Delta V=\left|\phi_{R}-\phi_{\infty}\right|$. Equation (4.8) indicates that the capacitance of an isolated charged sphere depends only on its radius $R$, and it is independent of both the charge $Q$ on the sphere and potential difference $\Delta V$.

C≡问Δ在

## 物理代写|电磁学代写electromagnetism代考|Calculating Capacitance

φ+−φ一个=−∫一个(+)和⋅ds

φ−−φ乙=−∫乙(−)和⋅ds

Δ在=|φ+−φ−|

## 物理代写|电磁学代写electromagnetism代考|Spherical Conductors

φR=ķ和问R

C=问¯Δ在=ķ和¯问/R=R¯ķ和=4圆周率ε0R

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。