# 电磁学代写 Electromagnetism代考2023

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## 电磁学代写Electromagnetism

### 经典电磁学Classical electrodynamics代写

1600年，威廉-吉尔伯特在他的De Magnete中提出，电和磁虽然都能引起物体的吸引和排斥，但却是不同的效果。海员们注意到，雷击有能力干扰罗盘针。直到本杰明-富兰克林在1752年提出的实验，法国的托马斯-弗朗索瓦-达利巴德在1752年5月10日用一根40英尺高（12米）的铁棒代替风筝进行了实验，他成功地从云中提取了电火花，这才证实了闪电和电力之间的联系。

• Nonlinear system非线性系统
• Magnetohydrodynamics磁流体力学

## 电磁学的历史

The earliest study of this phenomenon probably goes back to the Greek philosopher Thales (600 BC), who studied the electrical properties of amber, a fossil resin that attracts other substances when rubbed: its Greek name is elektron (ἤλεκτρον), from which the word ‘electricity’ is derived. The ancient Greeks realised that amber could attract light objects, such as hair, and that repeated rubbing of the amber itself could even produce sparks.

## 电磁学相关课后作业代写

Show that $S^4$ has no symplectic structure. Show that $S^2 \times S^4$ has no symplectic structure.

To show that $S^4$ has no symplectic structure, we will use the following fact from symplectic geometry: a compact symplectic manifold has even dimension.

Suppose that $S^4$ has a symplectic structure. Then $S^4$ is a compact symplectic manifold, so its dimension must be even. However, the dimension of $S^4$ is $4$, which is not even. Therefore, $S^4$ cannot have a symplectic structure.

To show that $S^2 \times S^4$ has no symplectic structure, we will use the following fact: the product of two symplectic manifolds is symplectic if and only if both factors have even dimension.

Suppose that $S^2 \times S^4$ has a symplectic structure. Then both $S^2$ and $S^4$ are symplectic manifolds, so their dimensions must both be even. However, the dimension of $S^2$ is $2$, which is not even. Therefore, $S^2 \times S^4$ cannot have a symplectic structure.

# 电磁学 Electromagnetism PHYS370

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where the group velocity
$$\mathbf{v}{g}=\nabla{\mathbf{k}{0} \mid} \omega\left(k{0}\right)=\frac{\mathbf{k}{0}}{\omega\left(\mathbf{k}{0}\right)} .$$
The last term in the exponent can be neglected if
$$\frac{q^{2}}{\omega}\left(t-t_{0}\right) \ll 1 \quad \text { or } \quad \frac{L \cdot(\Delta k)^{2}}{k_{0}} \ll 1,$$

## PHYS370 COURSE NOTES ：

$$h\left(\mathbf{x}-\mathbf{x}{0}-\mathbf{v}{g}\left(t-t_{0}\right)\right)=h\left(\rho, z-z_{0}-v_{g}\left(t-t_{0}\right)\right)$$
and
\begin{aligned} \frac{d \mathbf{W}}{d A} &=\frac{\omega_{0} \mathbf{k}{0}}{2 \pi} \int d t\left[h\left(\boldsymbol{\rho}, z-z{0}-v_{g}\left(t-t_{0}\right)\right)\right]^{2} \ &=\frac{\omega_{0}^{2} \hat{k}{0}}{2 \pi} \int{-\infty}^{\infty} d z h^{2}(\boldsymbol{\rho}, z) \end{aligned}
where
$$\boldsymbol{\rho}=\hat{\mathbf{e}}{x} x+\hat{\mathbf{e}}{y} y$$
With $\rho$ located at the target transverse coordinate, that is, $\rho=0$, we have
$$\frac{d \mathbf{W}}{d A}=\frac{\omega_{0}^{2} \hat{\mathbf{k}}{0}}{2 \pi} \int{-\infty}^{\infty} d z h^{2}(\mathbf{0}, z)$$

# 电磁学 Electromagnetism PHYS201

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The special case of a point charge at the origin, for which $\rho=q \delta(\mathbf{r})$ and $\mathbf{E}=q\left(\mathbf{r} / r^{3}\right)$, shows that $\nabla \cdot\left(\mathbf{r} / r^{3}\right)$ acts as if
$$\nabla \cdot \frac{\mathbf{r}}{r^{3}}=4 \pi \delta(\mathbf{r})$$
yields an equation for the electrostatic potential $\phi:$
$$\nabla \cdot \mathbf{E}=-\nabla \cdot \Gamma \phi=4 \pi \rho \quad \text { or } \quad \nabla^{2} \phi=-4 \pi \rho .$$
This is known as Poisson’s equation. In a portion of space where $\rho=0$, becomes
$$\nabla^{2} \phi=0$$

## PHYS201COURSE NOTES ：

$$\psi_{0}(\mathbf{x}, 0)=e^{i \mathbf{k}{0}-\left(\mathbf{x}-\mathbf{x}{0}\right)} h\left(\mathbf{x}-\mathbf{x}{0}\right)+\text { c.c. }$$ where $$h\left(\mathbf{x}-\mathbf{x}{0}\right)=\int d \mathbf{q} a(\mathbf{q}) e^{i \mathbf{q} \cdot\left(\mathbf{x}-\mathbf{x}_{0}\right)}$$

# 电磁学|PH30077/PH30078 Electromagnetism 2/Magnetism代写

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$$\frac{\epsilon-1}{\epsilon+2}=\frac{4 \pi}{3} n \alpha$$
where $\alpha$ is the atomic polarizability and $n$ the number of atoms per unit volume. This formula predicts that the measurable quantity
$$\frac{(\epsilon+2) n}{\epsilon-1}$$
for a given substance should be approximately independent of external parameters, such as pressure and temperature. Note that weak coupling between the atoms corresponds to small $n \alpha$, so that
$$\epsilon-1 \cong 4 \pi n \alpha .$$

## PH30077/PH30078 COURSE NOTES ：

$$\mathbf{F}{\mathrm{Con} p}=p \mathbf{B}=-\frac{I}{c} \oint d \mathbf{I}^{\prime} \times p \frac{\left(\mathbf{r}^{\prime}-\mathbf{r}\right)}{\left|\mathbf{r}-\mathbf{r}^{\prime}\right|^{3}}$$ We recognize $$p \frac{\left(\mathbf{r}^{\prime}-\mathbf{r}\right)}{\left|\mathbf{r}-\mathbf{r}^{\prime}\right|^{3}}=\mathbf{B}{p}\left(\mathbf{r}^{\prime}\right)$$
where $\mathbf{B}{p}\left(\mathbf{r}^{\prime}\right)$ is the magnetic field that would be produced at $\mathbf{r}^{\prime}$ by the hypothetical pole at $\mathbf{r}$. Thus, $$\mathbf{F}{C \text { on } p}=-\frac{I}{c} \oint d \mathbf{l}^{\prime} \times \mathbf{B}_{p}\left(\mathbf{r}^{\prime}\right),$$

# 电磁学|PH20014/PH20061 Electromagnetism 1代写

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which is simply the Klein-Gordon equation
$$\left[\eta^{a b} p_{a} p_{b}+m_{e f f}^{2}\right] \psi=0$$
with a mass term
$$m_{e f f}^{2}=\frac{2 \mathcal{E}}{D+1} m^{2}$$
Non-stationary states are superpositions of Klein-Gordon states with different values of $m_{e f f}^{2}$. It can be shown that as long as we only superimpose states with $\varepsilon>0$, i.e. $m_{e f f}^{2}>0$ non-tachyonic, the wavepacket follows a timelike trajectory.
Next, consider minisuperspace models of the form

## PPH20014/PH20061 COURSE NOTES ：

$$\phi=\frac{q}{|\mathbf{r}-\mathbf{b}|}+\delta \phi$$
wherc
$$\delta \phi=-q \frac{a}{b} \frac{(\epsilon-1)}{\epsilon+1} I$$
with
$$I=\frac{1}{\left(1+y^{2}-2 y \cos \theta\right)^{1 / 2}}-\frac{1}{\gamma y^{1 / \gamma}} \int_{0}^{\gamma} d y^{\prime} \frac{\left(y^{\prime}\right)^{1 / \gamma-1}}{\left(1+y^{\prime 2}-2 y^{\prime} \cos \theta\right)^{1 / 2}}$$

# 电磁学作业代写Electromagnetism代考

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## 电磁单元Electromagnetic units 代写

• 强相互作用Strong interaction
• 弱相互作用Weak interaction
• 分子间作用力Intermolecular force
• 磁流体力学Magnetohydrodynamics

## 电磁学的历史

Originally, electricity and magnetism were considered to be two separate forces. This view changed with the publication of James Clerk Maxwell’s 1873 A Treatise on Electricity and Magnetism [2]in which the interactions of positive and negative charges were shown to be mediated by one force. There are four main effects resulting from these interactions, all of which have been clearly demonstrated by experiments

## 电磁学课后作业代写

The scalar Wiener process $W(t)$ is defined by the following properties:

1. $W(t)$ satisfies the following initial condition:
$$W(0)=0$$
2. $W(t)-W(s)$, with $t>s \geq 0$, is a gaussian random variable with zero mean and variance $t-s$ :
$$\left\langle\left[W\left(t_{1}\right)-W\left(s_{1}\right)\right]^{2}\right\rangle=t-s$$
3. $W(t)$ has uncorrelated increments:
$$\left\langle\left[W\left(t_{1}\right)-W\left(s_{1}\right)\right]\left[W\left(t_{2}\right)-W\left(s_{2}\right)\right]\right\rangle=0$$
when $0 \leq s_{2}<t_{2} \leq s_{1}<t_{1} .$