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电磁学是电荷、磁矩和电磁场之间的物理互动。电磁场可以是静态的，缓慢变化的，或形成波。电磁波一般被称为光，遵守光学定律。
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我们提供的电磁学electromagnetism及其相关学科的代写，服务范围广, 其中包括但不限于:
- 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|Effects of non-uniform resistivity
Two geometrically identical cylindrical conductors have both height $h$ and radius $a$, but different resistivities $\rho_{1}$ and $\rho_{2}$. The two cylinders are connected in series as in Fig. 4.6, forming a single conducting cylinder of height $2 h$ and cross section $S=\pi a^{2}$. The two opposite bases are connected to a voltage source maintaining a potential difference $V$ through the system, as shown in the figure.
a) Evaluate the electric fields, the electric current and the current densities flowing in the two cylinders in stationary conditions.
b) Evaluate the surface charge densities at the surface separating the two materials, and at the base surfaces connected to the voltage source.
A spherical capacitor has internal radius $a$ and external radius $b$. The spherical shell $a<$ $r<b$ is filled by a lossy dielectric medium of relative dielectric permittivity $\varepsilon_{\mathrm{r}}$ and conductivity $\sigma$. At time $t=0$, the charge of the capacitor is $Q_{0}$.
a) Evaluate the time constant for the discharge of the capacitor.
b) Evaluate the power dissipated by Joule heating inside the capacitor, and compare it with the temporal variation of the electrostatic energy.
物理代写|电磁学代写electromagnetism代考|Magnetostatics
Topics. Stationary magnetic field in vacuum. Lorentz force. Motion of an electric point charge in a magnetic field. The magnetic force on a current. The magnetic field of steady currents. “Mechanical” energy of a circuit in a magnetic field. Biot-Savart law. Ampères’ circuital law. The magnetism of matter. Volume and surface magnetization current densities (bound currents). Magnetic susceptibility. The “auxiliary” vector H. Magnetic field boundary conditions. Equivalent magnetic charge method.
Units. In order to write formulas compatible with both SI and Gaussian units, we introduce two new “system dependent” constants, $k_{\mathrm{m}}$ and $b_{\mathrm{m}}$, defined as
$$
k_{\mathrm{m}}=\left{\begin{array}{ll}
\frac{\mu_{0}}{4 \pi}, & \mathrm{Sl}, \
\frac{1}{c}, & \text { Gaussian, }
\end{array} \quad b_{\mathrm{m}}= \begin{cases}1, & \text { SI } \
\frac{1}{c}, & \text { Gaussian },\end{cases}\right.
$$
where, again, $\mu_{0}=4 \pi \times 10^{-7} \mathrm{~T} \cdot \mathrm{m} / \mathrm{A}$ is the “magnetic permeability of vacuum”, and $c=29979245800 \mathrm{~cm} / \mathrm{s}$ is the light speed in vacuum.
Basic equations The two Maxwell equations for the magnetic field $\mathbf{B}$ relevant to this chapter are
$$
\begin{aligned}
\boldsymbol{\nabla} \cdot \mathbf{B} &=0 \
\boldsymbol{\nabla} \times \mathbf{B} &=4 \pi k_{\mathrm{m}} \mathbf{J}
\end{aligned}
$$
Equation (5.2) is always valid (in the absence of magnetic monopoles), while (5.3) is valid in the absence of time-dependent electric fields. It is thus possible to introduce a vector potential $\mathbf{A}$, such that
$$
\mathbf{B}(\mathbf{r})=\boldsymbol{\nabla} \times \mathbf{A}(\mathbf{r}),
$$
Imposing the gauge condition $\boldsymbol{\nabla} \cdot \mathbf{A}=0$, the vector potential satisfies
$$
\nabla^{2} \mathbf{A}(\mathbf{r})=-4 \pi k_{\mathrm{m}} \mathbf{J}(\mathbf{r})
$$
which is the vector analogous of Poisson’s equation (2.1). Thus,
$$
\mathbf{A}(\mathbf{r})=k_{\mathrm{m}} \int_{V} \frac{\mathbf{J}\left(\mathbf{r}^{\prime}\right)}{\left|\mathbf{r}-\mathbf{r}^{\prime}\right|} \mathrm{d}^{3} r^{\prime}
$$
物理代写|电磁学代写electromagnetism代考|The Rowland Experiment
This experiment by Henry A. Rowland (1876) aimed at showing that moving charges generate magnetic fields. A metallic disk or radius $a$ and thickness $b \ll a$ is electrically charged and kept in rotation with a constant angular velocity $\omega$.
a) The disk rotates between two conducting plates, one at a distance $h \simeq 0.5 \mathrm{~cm}$ above its upper surface, and the other at $h$ below its lower surface, as in Fig. 5.1. The two plates are connected to the same terminal of a voltage source maintaining a potential difference $V_{0}=10^{4} \mathrm{~V}$, while the other terminal is connected to the disk by a sliding contact. Evaluate the surface charge density on the disk surfaces.
b) Calculate the magnetic field $\mathbf{B}{\mathrm{c}}$ near the center of the disk and the magnetic field component $B{r}$ parallel and close to the disk surfaces, as a function of the distance $r$ from the axis. Typical experimental values were $a=10 \mathrm{~cm}$, and $\omega \simeq 2 \pi \times 10^{2} \mathrm{rad} / \mathrm{s}$ (period $T=2 \pi / \omega=10^{-2} \mathrm{~s}$ ).
c) The field component $B_{r}$ generated by the disk at $r=a$ can be measured by orienting the apparatus so that $\hat{\mathbf{r}}$ is perpendicular to the Earth’s magnetic field $\mathbf{B}{\oplus}$, of strength $B{\oplus} \simeq 5 \times 10^{-5} \mathrm{~T}$, and measuring the deviation of a magnetic needle when the disk rotates. Find the deviation angle of the needle.
电磁学代考
物理代写|电磁学代写electromagnetism代考|Effects of non-uniform resistivity
两个几何形状相同的圆柱形导体具有两个高度 $h$ 和半径 $a$, 但不同的电阻率 $\rho_{1}$ 和 $\rho_{2}$. 两个圆柱体串联连接，如图 $4.6$ 所示，形成一个高度为 $2 h$ 和横載面 $S=\pi a^{2}$. 两个相对的基极连接到保持电位差的电压源 $V$ 通过系统，如图所示。
a) 评估静止条件下两个圆柱体中流动的电场、电流和电流密度。
b) 评估分离两种材料的表面以及连接到电压源的基面的表面电荷密度。
球形电容器具有内半径 $a$ 和外半径 $b$. 球壳 $a<r<b$ 由具有相对介电常数的有损电介质填充 $\varepsilon_{\mathrm{r}}$ 和电导率 $\sigma$. 当时 $t=0$ ，电容器的电荷为 $Q_{0}$.
a) 评估电容器放电的时间常数。
b) 评估电容㕷内部焦耳热耤散的功率，并将其与静电能量的时间变化进行比较。
物理代写|电磁学代写electromagnetism代考|Magnetostatics
话题。真空中的固定磁场。洛伦兹力。点电荷在磁场中的运动。电流上的磁力。稳定电流的磁场。磁场中电路的”机械”能量。Biot-Savart 定律。安培电路定律。物质的磁性。体稆和表面砯化电流密度 (束俌电流)。磁化率。”辅助”矢量 $H$. 磁场边界条件。等效磁荷法。 单位。为了编写与 $\mathrm{SI}$ 和高斯单位兼容的公式，我们引入了两个新的”系统相关”常数， $k_{\mathrm{m}}$ 和 $b_{\mathrm{m}}$ 定义为
$\$ \$$
$k_{-} \wedge$ mathrm $\left.{\mathrm{m}}\right}=\backslash$ left {
$\frac{\mu_{0}}{4 \pi}, \quad \mathrm{Sl}, \frac{1}{c}, \quad$ Gaussian,
$\backslash$ quad b_气mathrm{m}}=
$\left{1, \quad\right.$ SI $\frac{1}{c}, \quad$ Gaussian
正确的。
$\$ \$$
在哪里，再次， $\mu_{0}=4 \pi \times 10^{-7} \mathrm{~T} \cdot \mathrm{m} / \mathrm{A}$ 是“真空的磁导率”，并且 $c=29979245800 \mathrm{~cm} / \mathrm{s}$ 是真空中的光速。
基本方程 磁场的两个麦克斯韦方程 $\mathbf{B}$ 与本章相关的是
$$
\boldsymbol{\nabla} \cdot \mathbf{B}=0 \boldsymbol{\nabla} \times \mathbf{B} \quad=4 \pi k_{\mathrm{m}} \mathbf{J}
$$
方程（5.2）总是有效的（在没有磁单极子的情呪下），而 (5.3) 在没有时间相关电场的情况下是有效的。因此可以引入矢量势 $\mathbf{A}$, 这样
$$
\mathbf{B}(\mathbf{r})=\boldsymbol{\nabla} \times \mathbf{A}(\mathbf{r}),
$$
施加仪表条件 $\boldsymbol{\nabla} \cdot \mathbf{A}=0$, 向量勢满足
$$
\nabla^{2} \mathbf{A}(\mathbf{r})=-4 \pi k_{\mathrm{m}} \mathbf{J}(\mathbf{r})
$$
这是类似于泊松方程 (2.1) 的向量。因此，
$$
\mathbf{A}(\mathbf{r})=k_{\mathrm{m}} \int_{V} \frac{\mathbf{J}\left(\mathbf{r}^{\prime}\right)}{\left|\mathbf{r}-\mathbf{r}^{\prime}\right|} \mathrm{d}^{3} r^{\prime}
$$
物理代写|电磁学代写electromagnetism代考|The Rowland Experiment
亨利 A. 罗兰 (Henry A. Rowland)（1876 年）的这项实验旨在证明移动电荷会产生磁场。金属圆盘或半径 $a$ 和厚度 $b \ll a$ 带电并以恒定角速 度保持旋转 $\omega$.
a) 圆盘在两块导电板之间旋转，一块在一定距离处 $h \simeq 0.5 \mathrm{~cm}$ 在其上表面之上，另一个在 $h$ 低于其下表面，如图 $5.1$ 所示。两个板连接到 保持电位差的电压源的同一端子 $V_{0}=10^{4} \mathrm{~V}$ ，而另一个端子通过滑动触点连接到磁盘。评估磁盘表面的表面电荷密度。
b) 计算磁场 $\mathrm{Bc} \mathrm{c}$ 靠近磁盘中心和磁场分量 $B r$ 平行和靠近磁盘表面，作为距离的函数 $r$ 从轴。典型的实验值是 $a=10 \mathrm{~cm}$ ，和
$\omega \simeq 2 \pi \times 10^{2} \mathrm{rad} / \mathrm{s}$ (时期 $T=2 \pi / \omega=10^{-2} \mathrm{~s}$ )。
c) 字段組件 $B_{r}$ 由磁盘在 $r=a$ 可以通过调整设备的方向来测量全垂直于地球碰场 $\mathbf{B} \oplus$ ，强度 $B \oplus \simeq 5 \times 10^{-5} \mathrm{~T}$ ，并测量磁盘旋转时磁针的
偏差。求出针的偏角。
