## 物理代写|电动力学代写electromagnetism代考|SOME FUNDAMENTAL IDEAS

At about the same time that Coulomb was examining the force between isolated charges, he was also experimenting with magnetism (1785). In common with electrostatics, he found that the force between two magnetic poles decreases as the inverse of the square of the distance separating them, i.e.,
$$\boldsymbol{F}=\frac{p_1 p_2}{k r^2} \boldsymbol{r}$$
where
$F$ is the vector force between the two poles $(\mathrm{N})$
$p_1$ and $\mathrm{p}_2$ are the strengths of the magnetic poles $(\mathrm{Wb})$
$k$ is a constant of proportionality
$r$ is the distance between two poles $(\mathrm{m})$ and
$r$ is the unit vector acting in the direction of the line joining the two charges
This is the exact parallel of Coulomb’s law as applied to isolated point charges. The force is repulsive if the poles are alike and attractive if the poles are dissimilar (Figure 3.1).
We can extract a factor of $4 \pi$ from the constant $k$ to give
$$\boldsymbol{F}=\underset{4 \pi \mu r^2}{p_1 p_2} \boldsymbol{r}$$
where $\mu$ is the permeability – a material property. If we use the SI system of units, the force is in Newton if the pole strengths are in Weber (named after Wilhelm Eduard Weber, 1804-1891, the German physicist noted for his study of terrestrial magnetism), $\mu$ is in $\mathrm{H} \mathrm{m}^{-1}$ and $r$ is in metre. The reason for the choice of units for $\mu$ will become clear when we consider inductance in Section 3.11.

## 物理代写|电动力学代写electromagnetism代考|SOME ELEMENTARY CONVENTIONS

Having established that the inverse square law applies to isolated magnetic monopoles, we will now examine the magnetic field produced by a current-carrying conductor. (Although readers may not be very familiar with this effect, everyone has come across it. Any piece of rotating electrical equipment – power tools, alternators, starter motors, etc., – relies on the magnetic fields produced by a current-carrying wire. We will consider a simple motor/generator in Chapter 7.)

In 1819, Hans Christian Oersted (a Danish physicist) demonstrated that a magnetic field surrounds a current-carrying wire. This was a very important discovery because it unified the separate sciences of electricity and magnetism into one science – electromagnetism. (Indeed, this was the first indication that two different forces of Nature could be unified. The search is now on for a Grand Unified Theory that would explain life, the Universe and everything!)

Oersted plotted the field surrounding a current-carrying wire using a compass. As Figure $3.2$ shows, the magnetic field is coaxial to the wire. The direction of the field depends on whether the current flows up, as in Figure 3.2a, or down the wire, as in Figure $3.2 \mathrm{~b}$.
We now come across some conventions:

1. A cross denotes current flowing into the page. A dot denotes current flowing out of the page.
Figure $3.2 \mathrm{c}$ shows these two conventions.
Readers who play darts might like to imagine a dart thrown into the page. As the dart travels away from us, we see the cross of the feathers. Thus, a cross denotes current travelling away from us, down the wire. If the dart is travelling towards us, we see the point of the dart first – until it hits us! Hence, a dot corresponds to current travelling towards us, up the wire.
2. The right-hand corkscrew rule gives the direction of the flux.
Figure $3.2 \mathrm{c}$ shows this rule.
Most of us are familiar with the action of a corkscrew. We can use this action to determine the direction of the magnetic field. If we have current flowing away from us into the page, a corkscrew will have to turn in a clockwise direction to follow the current. Thus, the field acts in a clockwise direction. If the current is flowing towards us out of the page, the corkscrew acts in an anticlockwise direction. Thus, the field acts in an anticlockwise direction.

## 物理代写|电动力学代写electromagnetism代考|SOME FUNDAMENTAL IDEAS

$$\boldsymbol{F}=\frac{p_1 p_2}{k r^2} \boldsymbol{r}$$

$F$ 是两极之间的矢量力 $(\mathrm{N})$
$p_1$ 和 $\mathrm{p}_2$ 是磁极的强度 $(\mathrm{Wb})$
$k$ 是比例常数
$r$ 是两极之间的距离 $(\mathrm{m})$ 和
$r$ 是作用在连接两个电荷的线方向上的单位矢量

$$\boldsymbol{F}=\underset{4 \pi r^2}{p_1 p_2} \boldsymbol{r}$$

## 物理代写|电动力学代写electromagnetism代考|SOME ELEMENTARY CONVENTIONS

1819 年，汉斯·克里斯蒂安·奥斯特（丹麦物理学家）证明了磁场围绕着载流导线。这是一个非常重要的发现，因为它将电学和磁学这两个独立的科学统一为一门科学——电磁学。（事实上​​，这是两种不同的自然力量可以统一的第一个迹象。现在正在寻找一个可以解释生命、宇宙和一切的大统一理论！）

1. 十字表示流入页面的电流。点表示流出页面的电流。
数字3.2C显示这两个约定。
玩飞镖的读者可能会想像一个飞镖扔进页面。当飞镖远离我们时，我们看到了羽毛的十字架。因此，十字表示电流远离我们，沿着电线流过。如果飞镖朝我们飞来，我们首先会看到飞镖的尖端——直到它击中我们！因此，一个点对应于沿着电线向我们流动的电流。
2. 右手开瓶器规则给出了通量的方向。
数字3.2C显示此规则。
我们大多数人都熟悉开瓶器的动作。我们可以使用这个动作来确定磁场的方向。如果我们有电流从我们身边流入页面，开瓶器将不得不顺时针方向转动以跟随电流。因此，该场沿顺时针方向起作用。如果电流从页面流向我们，则开瓶器以逆时针方向作用。因此，该场以逆时针方向作用。

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