### 物理代写|电磁学代写electromagnetism代考|PHYS3040

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
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (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|Mie Oscillations

Now, instead of a the metal slab of Problem 1.4, consider a metal sphere of radius $R$. Initially, all the conduction electrons ( $n_{\mathrm{e}}$ per unit volume) are displaced by $-\delta$ (with $\delta \ll R$ ) by an external electric field, analogously to Problem 1.1.
a) At time $t=0$ the external field is suddenly removed. Describe the subsequent motion of the conduction electrons under the action of the self-consistent electrostatic field, neglecting the boundary effects on the electrons close to the surface of the sphere.
b) At the limit $\delta \rightarrow 0$ (but assuming $e n_{\mathrm{e}} \delta=\sigma_{0}$ to remain finite, $\mathrm{i}{2} \mathrm{e}{2}$, the charge distribution is a surface density), find the electrostatic energy of the sphere as a function of $\delta$ and use the result to discuss the electron motion as in point $\mathbf{a})$.

## 物理代写|电磁学代写electromagnetism代考|Coulomb explosions

At $t=0$ we have a spherical cloud of radius $R$ and total charge $Q$, comprising $N$ point-like particles. Each particle has charge $q=Q / N$ and mass $m$. The particle density is uniform, and all particles are at rest.

a) Evaluate the electrostatic potential energy of a charge located at a distance $r0$. Consider the particles located in the infinitesimal spherical shell $r_{0}<r_{\mathrm{s}}<r_{0}+\mathrm{d} r$, with $r_{0}+\mathrm{d} r<R$, at $t=0$. Show that the equation of motion of the layer is
$$m \frac{\mathrm{d}^{2} r_{\mathrm{s}}}{\mathrm{d} t^{2}}=k_{\mathrm{e}} \frac{q Q}{r_{\mathrm{s}}^{2}}\left(\frac{r_{0}}{R}\right)^{3}$$
c) Find the initial position of the particles that acquire the maximum kinetic energy during the cloud expansion, and determinate the value of such maximum energy.
d) Find the energy spectrum, i.e., the distribution of the particles as a function of their final kinetic energy. Compare the total kinetic energy with the potential energy initially stored in the electrostatic field.
e) Show that the particle density remains spatially uniform during the expansion.

## 物理代写|电磁学代写electromagnetism代考|Plane and Cylindrical Coulomb Explosions

Particles of identical mass $m$ and charge $q$ are distributed with zero initial velocity and uniform density $n_{0}$ in the infinite slab $|x|0$ the slab expands because of the electrostatic repulsion between the pairs of particles.
a) Find the equation of motion for the particles, its solution, and the kinetic energy acquired by the particles.
b) Consider the analogous problem of the explosion of a uniform distribution having cylindrical symmetry.

Two rigid spheres have the same radius $R$ and the same mass $M$, and opposite charges $\pm Q$. Both charges are uniformly and rigidly distributed over the volumes of the two spheres. The two spheres are initially at rest, at a distance $x_{0} \gg R$ between their centers, such that their interaction energy is negligible compared to the sum of their “internal” (construction) energies.
a) Evaluate the initial energy of the system.
The two spheres, having opposite charges, attract each other, and start moving at $t=0$.
b) Evaluate the velocity of the spheres when they touch each other (i.e. when the distance between their centers is $x=2 R$ ).
c) Assume that, after touching, the two spheres penetrate each other without friction. Evaluate the velocity of the spheres when the two centers overlap $(x=0)$.

An electrically neutral metal sphere of radius $a$ contains $N$ conduction electrons. A fraction $f$ of the conduction electrons $(0<f<1)$ is removed from the sphere, and the remaining $(1-f) N$ conduction electrons redistribute themselves to an equilibrium configurations, while the $N$ lattice ions remain fixed.
a) Evaluate the conduction-electron density and the radius of their distribution in the sphere.

Now the conduction-electron sphere is rigidly displaced by $\boldsymbol{\delta}$ relatively to the ion lattice, with $|\delta|$ small enough for the conduction-electron sphere to remain inside the ion sphere.
b) Evaluate the electric field inside the conduction-electron sphere.
c) Evaluate the oscillation frequency of the conduction-electron sphere when it is released.

## 物理代写|电磁学代写electromagnetism代考|Mie Oscillations

a) 有时吨=0外场突然被移除。描述导电电子在自洽静电场作用下的后续运动，忽略靠近球体表面的电子的边界效应。
b) 在极限d→0（但假设和n和d=σ0保持有限，一世2和2，电荷分布是表面密度），找到球体的静电能量作为函数d并使用结果来讨论电子运动一个).

## 物理代写|电磁学代写electromagnetism代考|Coulomb explosions

a) 评估位于远处的电荷的静电势能r0. 考虑位于无穷小球壳中的粒子r0<rs<r0+dr， 和r0+dr<R， 在吨=0. 证明层的运动方程为

c) 找出在云膨胀过程中获得最大动能的粒子的初始位置，并确定该最大能量的值。
d) 找出能谱，即粒子的分布作为其最终动能的函数。将总动能与最初存储在静电场中的势能进行比较。
e) 表明粒子密度在膨胀过程中保持空间均匀。

## 物理代写|电磁学代写electromagnetism代考|Plane and Cylindrical Coulomb Explosions

a) 找出粒子的运动方程、它的解以及粒子获得的动能。
b) 考虑具有圆柱对称性的均匀分布爆炸的类似问题。

a) 评估系统的初始能量。

b) 评估球体相互接触时的速度（即，当它们的中心之间的距离为X=2R）。
c) 假设两个球体接触后相互穿透，没有摩擦。计算两个中心重叠时球体的速度(X=0).

a) 评估传导电子密度及其在球体中的分布半径。

b) 评估传导电子球内的电场。
c) 评估传导电子球释放时的振荡频率。

## 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。