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

# 物理代写|电磁学代写Electromagnetism代考|PHYS404 Magnetic Moments of Atoms

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|Magnetic Moments of Atoms

The magnetic field created by a current-carrying coil of wire can explain what makes some materials to have strong magnetic properties. In general, based on Biot-Savart law (Eq. (7.1), Chap. 7), any current loop produces a magnetic field, as shown in Fig. 8.1. Thus, it has a magnetic dipole moment, including the atomic-level current loops described in some models of the atom. Those atomic-level current loops may define the magnetic moments in a magnetized substance. In the Bohr model of the atom, the current loops are associated with the circular motion of electrons around the nucleus. Besides, another magnetic moment, which is intrinsic to electrons, protons, neutrons, and other particles, arises from a property called spin.

Now, let us consider the classical model of the atom in which electrons move in circular orbits around the nucleus. Each orbiting electron creates a current loop because it is a moving charge $e$. Therefore, there exists a magnetic moment of the electron associated with its orbital motion (see also Fig. 8.2). Suppose electron is moving with constant speed $v$ in a circular orbit of radius $r$ about the nucleus counterclockwise, as shown in Fig. 8.2. During a full period $T$, the electron travels the length $2 \pi r$, which is the circumference of the circle, and hence its speed is
$$v=\frac{2 \pi r}{T}$$
The current $I$ associated with this orbiting electron with a charge $e$ is given as
$$I=\frac{e}{T}$$
Using the following relations:
\begin{aligned} T &=\frac{2 \pi}{\omega} \ \omega &=\frac{v}{r} \end{aligned}
we get
$$I=\frac{e \omega}{2 \pi}=\frac{e v}{2 \pi r}$$

## 物理代写|电磁学代写Electromagnetism代考|Magnetization Vector and Magnetic Field Strength

To describe the magnetic properties of a substance, the magnetization vector $\mathbf{M}$ is introduced. In a substance of volume $V$ with a large number of molecules or atoms per unit of volume, where each has a magnetic moment $\mu_i$, the average macroscopic magnetization vector is
$$\mathbf{M}(\mathbf{r})=\sum_i n_i\left\langle\boldsymbol{\mu}i\right\rangle$$ where $n_i$ is the average number density of molecules or atoms of type $i$ and $\left\langle\boldsymbol{\mu}_i\right\rangle$ is the average magnetic moment in a macroscopically small volume element centered at position $\mathbf{r}$ of type $i$. The magnetization contributes an effective current density: $$\mathbf{J}_M=\nabla \times \mathbf{M}$$ In the microscopic description, Ampére’s law for static electric fields can be rewritten as $$\oint{\mathcal{L}} \mathbf{B}{\text {micro }} \cdot d \mathbf{s}=\mu_0 \int_A \mathbf{J}{\text {micro }} \cdot d \mathbf{A}$$
where $A$ is any surface enclosed by the path $\mathcal{L}$. Using Stokes’ formula, we obtain
$$\int_A\left(\nabla \times \mathbf{B}{\text {micro }}\right) \cdot d \mathbf{A}=\mu_0 \int_A \mathbf{J}{\text {micro }} \cdot d \mathbf{A}$$

## 物理代写|电磁学代写Electromagnetism代考|Magnetic Moments of Atoms

$$v=\frac{2 \pi r}{T}$$

$$I=\frac{e}{T}$$

$$T=\frac{2 \pi}{\omega} \omega \quad=\frac{v}{r}$$

$$I=\frac{e \omega}{2 \pi}=\frac{e v}{2 \pi r}$$

## 物理代写|电磁学代写Electromagnetism代考|Magnetization Vector and Magnetic Field Strength

$$\mathbf{M}(\mathbf{r})=\sum_i n_i\langle\boldsymbol{\mu} i\rangle$$

$$\mathbf{J}_M=\nabla \times \mathbf{M}$$

$$\oint \mathcal{L} \mathbf{B m i c r o} \cdot d \mathbf{s}=\mu_0 \int_A \mathbf{J m i c r o} \cdot d \mathbf{A}$$

$$\int_A(\nabla \times \mathbf{B} \text { micro }) \cdot d \mathbf{A}=\mu_0 \int_A \mathbf{J m i c r o} \cdot d \mathbf{A}$$

## 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。