Posted on Categories:Electrodynamics, 物理代写, 电动力学

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## 物理代写|电动力学代考Electrodynamics代写|Drude theory of metals: Ohm’s law

The Lorentz model for dielectrics may be applied to conductors (metals or, generally for plasma), considering this case as a limit $\omega_0=0$. The result is achieved because of relaxation mechanism is taken into account. The limit may be interpreted as a transition to free electrons of a metal (generally free charges, ions or holes in a solid).
It is considered as a version of the Drude model [12] as a response of a conducting matter to a time-dependent electric field with an angular frequency $\omega$ (cf the DC case in the next section).
An opposite limit $\omega_0 \ll \omega$ may be studied for high frequencies.
The complex amplitude of oscillations in a case of a conductor is given by the formula
$$x_0=\frac{-e E_{0 x}}{m\left(\omega^2+i \gamma \omega\right)} .$$
We will consider relations for the complex amplitudes for the exponential form of solutions.

The polarization vector will hence have the form
$$\vec{P}=\frac{e^2 N}{m} \operatorname{Re}\left[\sum_k \frac{-1}{\omega^2+i \gamma_k \omega}\right] \vec{E},$$
while the dielectric permeability we represent as
$$\begin{gathered} \chi=-\frac{N e^2}{m} \sum_k \operatorname{Re}\left[\frac{1}{\omega^2+i \gamma_k \omega}\right] \ \varepsilon=1-\frac{4 \pi N e^2}{m} \sum_k \operatorname{Re}\left[\frac{1}{\omega^2+i \gamma_k \omega}\right] \end{gathered}$$

## 物理代写|电动力学代考Electrodynamics代写|On the DC Ohm law

The charge transport in the DC case is a nonequilibrium process hence in general theory such a relation as equation (6.79) is derived via the kinetic equation solution with averaging procedure application [5]. In textbooks there often used a simplified theory, that in my imagination can be understood as follows. The quasiparticle which represents the charge transport (say, electron, more precise-polaron) is moving in the phonon (quasiparticle of atom net oscillations) gas of a solid as a drop falling in air. After the start it is accelerated by constant electric field, but soon the acceleration decreases because the electric force is compensated by friction that is proportional to the electron velocity. The equation of motion (of a small sphere) hence is modeled as
$$m \frac{d \vec{v}}{d t}=e \vec{E}-6 \pi \mu R \vec{v},$$
where the second, Stokes drug term is proportional to the radius $R$ and dynamical viscosity $\mu$. The viscosity coefficient in turn is determined by properties of the gas, for example kinetic (Chapman-Enskog) theory for Maxwellian particles gives
$$\mu=n_p k_B T / \lambda,$$
where $n_p$ is the gas concentration, $k_B$-Boltzmann constant, $T$-temperature and the constant $\lambda$-collision integral eigenvalue.

# 电动力学代写

## 物理代写|电动力学代考Electrodynamics代写|Drude theory of metals: 欧姆定律 定律

$$x_0=\frac{-e E_{0 x}}{m\left(\omega^2+i \gamma\omega\right)} 。$$

$$\vec{P}=frac{e^2 N}{m}。\operatorname{Re}\left[\sum_k\frac{-1}{omega^2+i \gamma_k \omega}\right] \vec{E}。$$

$$\chi=-frac{N e^2}{m}。\sum_k operatorname{Re}\left[frac{1}{omega^2+i gamma_komega}\right] varepsilon=1-frac{4pi N e^2}{m}。\sum_k operatorname{Re}\left[\frac{1}{omega^2+i gamma_komega}\right] 。$$

## 物理代写|电动力学代考Electrodynamics代写|On the DC Ohm law

$$m\frac{d vec{v}}{d t}=e vec{E}-6 pi mu R vec{v}。$$

$$\黏度=n_p k_B T / \lambda$$

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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。