# 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 $0 \leq s_{2}<t_{2} \leq s_{1}<t_{1} .$