Posted on Categories:Electromagnetism, 物理代写, 电磁学

# 物理代写|电磁学代写Electromagnetism代考|Faraday’s Law of Magnetic Induction

avatest™

## avatest™帮您通过考试

avatest™的各个学科专家已帮了学生顺利通过达上千场考试。我们保证您快速准时完成各时长和类型的考试，包括in class、take home、online、proctor。写手整理各样的资源来或按照您学校的资料教您，创造模拟试题，提供所有的问题例子，以保证您在真实考试中取得的通过率是85%以上。如果您有即将到来的每周、季考、期中或期末考试，我们都能帮助您！

•最快12小时交付

•200+ 英语母语导师

•70分以下全额退款

## 物理代写|电磁学代写Electromagnetism代考|Induction by a Temporal Change of B

Consider a time dependent magnetic field described by the magnetic induction or also called the magnetic flux density $\mathbf{B}(\mathbf{r}, t)$ and a contour $C$, fixed in space. The contour may be implemented by an infinitely thin, conducting material. If $A$ is the area that $C$ circumscribes, then by our definition, eq. (1.66), the magnetic flux penetrating this area is
$$\phi=\int_A \mathbf{B}(\mathbf{r}, t) \bullet d \mathbf{A}$$
The time dependent magnetic field $\mathbf{B}(\mathbf{r}, t)$ induces an electric field $\mathbf{E}(\mathbf{r}, t)$, which can be described using eq. (1.68)
$$\nabla \times \mathbf{E}(\mathbf{r}, t)=-\frac{\partial}{\partial t} \mathbf{B}(\mathbf{r}, t)$$
The line integral of the electric field is given by the time derivative of the magnetic flux:
$$\oint_C \mathbf{E} \bullet d \mathbf{s}=\int_A(\nabla \times \mathbf{E}) \bullet d \mathbf{A}=-\int_A \frac{\partial \mathbf{B}}{\partial t} d \mathbf{A}=-\frac{\partial}{\partial t} \int_A \mathbf{B} \bullet d \mathbf{A}=-\frac{\partial \phi}{\partial t} .$$
Expressed in a different form, one writes

$$V_i=\oint_C \mathbf{E} \cdot d \mathbf{s}=-\frac{\partial \phi}{\partial t}$$
where $V_i$ is the voltage (EMF), induced within the closed loop. Figure 6.1 shows the direction of the induced field for an increasing and a decreasing $\mathbf{B}$-field, respectively.

## 物理代写|电磁学代写Electromagnetism代考|Induction through the Motion of the Conductor

Inside a magnetic field $\mathbf{B}$, the Lorentz force
$$\mathbf{F}=Q(\mathbf{v} \times \mathbf{B})$$
acts on a particle with charge $Q$, and velocity $\mathbf{v}$.
One can also explain this force as being the effect of an electric field $\mathbf{E}$ on a particle within a moving reference frame, where
$$\mathbf{E}=\mathbf{v} \times \mathbf{B}$$
If one now moves a closed conductor loop (made of infinitely thin wire) within a magnetic field that is constant in time, then the line integral along the path $S$ (Fig. 6.2) is

$$\oint_S \mathbf{E} \bullet d \mathbf{s}=\oint_S(\mathbf{v} \times \mathbf{B}) \bullet d \mathbf{s}=-\oint_S \mathbf{B} \bullet(\mathbf{v} \times d \mathbf{s})$$
While the conductor loop moves during the time period $d t$, the path element $d \mathbf{s}$ covers an area element $d \mathbf{A}$ (Fig. 6.2):
$$\mathbf{v} \times d \mathbf{s} d t=d \mathbf{A}$$
Therefore
$$V_i=\oint_S \mathbf{E} \bullet d \mathbf{s}=-\oint_S \mathbf{B} \bullet \frac{d \mathbf{A}}{d t}=-\frac{d}{d t} \int_A \mathbf{B} \bullet d \mathbf{A}=-\frac{\mathrm{d} \phi}{\mathrm{d} t},$$
where we have only considered the flux change based on motion of the loop within a constant $\mathbf{B}$ field. Temporal changes of $\mathbf{B}$ itself are currently excluded, as outlined above. Consequently, as a result of the Lorentz force, the temporal change of the magnetic flux $\phi$ in a closed loop is given by line integral $\oint \mathbf{E} \bullet d \mathbf{s}$ (compare (6.3) with (6.7)).

## 物理代写|电磁学代写Electromagnetism代考|Induction by a Temporal Change of B

$$\phi=\int_A \mathbf{B}(\mathbf{r}, t) \bullet d \mathbf{A}$$

$$\nabla \times \mathbf{E}(\mathbf{r}, t)=-\frac{\partial}{\partial t} \mathbf{B}(\mathbf{r}, t)$$

$$\oint_C \mathbf{E} \bullet d \mathbf{s}=\int_A(\nabla \times \mathbf{E}) \bullet d \mathbf{A}=-\int_A \frac{\partial \mathbf{B}}{\partial t} d \mathbf{A}=-\frac{\partial}{\partial t} \int_A \mathbf{B} \bullet d \mathbf{A}=-\frac{\partial \phi}{\partial t}$$

$$V_i=\oint_C \mathbf{E} \cdot d \mathbf{s}=-\frac{\partial \phi}{\partial t}$$

## 物理代写|电磁学代写Electromagnetism代考|Induction through the Motion of the Conductor

$$\mathbf{F}=Q(\mathbf{v} \times \mathbf{B})$$

$$\mathbf{E}=\mathbf{v} \times \mathbf{B}$$

$$\oint_S \mathbf{E} \bullet d \mathbf{s}=\oint_S(\mathbf{v} \times \mathbf{B}) \bullet d \mathbf{s}=-\oint_S \mathbf{B} \bullet(\mathbf{v} \times d \mathbf{s})$$

$$\mathbf{v} \times d \mathbf{s} d t=d \mathbf{A}$$

$$V_i=\oint_S \mathbf{E} \bullet d \mathbf{s}=-\oint_S \mathbf{B} \bullet \frac{d \mathbf{A}}{d t}=-\frac{d}{d t} \int_A \mathbf{B} \bullet d \mathbf{A}=-\frac{\mathrm{d} \phi}{\mathrm{d} t},$$

## 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。