Electric Charge and Electric Force · 电荷与静电力
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| electric force/ɪˈlektrɪk fɔːs/ | 电力 | diàn lì |
| electric charge/ɪˈlektrɪk tʃɑːdʒ/ | 电荷 | diàn hè |
| coulombs/ˈkuːlɒmz/ | 库仑 | kù lún |
| quantised/ˈkwɒntaɪzd/ | 量子化 | liàng zǐ huà |
| Coulomb's law/ˈkuːlɒmz lɔː/ | 库仑定律 | kù lún dìng lǜ |
| inverse-square law/ɪnˈvɜːs skweə lɔː/ | 平方反比 | píng fāng fǎn bǐ |
| superposition/ˌsuːpəpəˈzɪʃn/ | 叠加 | dié jiā |
Why does a rubbed balloon stick to the wall?
- Rub a balloon on your hair and it clings to the wall — an invisible pull.
- That pull is the electric force 电力, one of the four fundamental forces.
- It acts between any objects that carry electric charge 电荷.
- This whole unit is built on one simple law for that force.
为什么摩擦过的气球会贴在墙上?
- 把气球在头发上摩擦,它就会贴在墙上——一种看不见的吸引。
- 这个吸引就是电力,是四种基本力之一。
- 它作用在任何带有电荷的物体之间。
- 整个单元都建立在描述这个力的一条简单定律上。
Two kinds of charge
- Charge comes in two kinds: positive and negative.
- Like charges repel; opposite charges attract.
- Charge is measured in coulombs 库仑 (C); the smallest free charge is the electron's, $e = 1.6\times10^{-19}$ C.
- Charge is quantised 量子化 (a whole number of $e$) and conserved — never created or destroyed.
两种电荷
- 电荷有两种:正电荷和负电荷。
- 同种电荷相斥;异种电荷相吸。
- 电荷用库仑(C)来量度;最小的自由电荷是电子的,$e = 1.6\times10^{-19}$ C。
- 电荷是量子化的(是 $e$ 的整数倍),并且守恒——既不产生也不消灭。
Two negative charges are brought near each other. They: · 两个负电荷相互靠近时，它们会：
Like charges repel — two negatives push apart. · 同种电荷相斥——两个负电荷互相推开。
Electric charge is measured in a unit called the . · 电荷的测量单位称为。
Charge is measured in coulombs (C). · 电荷以库仑（C）为单位计量。
Coulomb's law
- The force between two point charges follows Coulomb's law 库仑定律.
- $F = \dfrac{k\,q_1 q_2}{r^2}$, with $k = 8.99\times10^9\ \text{N}\cdot\text{m}^2/\text{C}^2$.
- The force points along the line joining the two charges.
- Bigger charges give a bigger force; greater separation gives a weaker one.
库仑定律
- 两个点电荷之间的力遵循库仑定律。
- $F = \dfrac{k\,q_1 q_2}{r^2}$,其中 $k = 8.99\times10^9\ \text{N}\cdot\text{m}^2/\text{C}^2$。
- 力沿着两电荷的连线方向。
- 电荷越大力越大;相距越远力越弱。
Two $+3\ \mu\text{C}$ charges are $2\ \text{m}$ apart. Find the force (in N). Use $k = 9\times10^9$. · 两个$+3\ \mu\text{C}$电荷相距$2\ \text{m}$。求作用力（单位：N）。使用$k = 9\times10^9$。
$F = \dfrac{(9\times10^9)(3\times10^{-6})^2}{2^2} = \dfrac{9\times10^9 \cdot 9\times10^{-12}}{4} \approx 0.02\ \text{N}$.
You double one · 一个 of the two charges. The force between them: · 你将其中一个电荷加倍。它们之间的作用力：
$F \propto q_1 q_2$, so doubling one charge doubles the force. · $F \propto q_1 q_2$，因此将一个电荷加倍会使作用力加倍。
An inverse-square law
- The $r^2$ on the bottom makes this an inverse-square law 平方反比.
- Double the distance and the force drops to a quarter.
- Triple the distance and it drops to a ninth.
- The very same $1/r^2$ shape returns later in gravity.
平方反比定律
- 分母上的 $r^2$ 使它成为一条平方反比定律。
- 距离加倍,力就降到四分之一。
- 距离变三倍,力就降到九分之一。
- 同样的 $1/r^2$ 形式稍后在引力中再次出现。
Coulomb's law · 库仑定律
The force between two charges falls off with the square of their separation (an inverse-square law). · 两个电荷之间的作用力随其分离距离的平方而下降（平方反比定律）。
If you triple the distance between two charges, the force drops to one ninth. · 若将两电荷间的距离扩大三倍，作用力降为原来的九分之一。
Force goes as $1/r^2$, so $\times 3$ distance means $\div 9$ force. · 作用力与$1/r^2$成反比，因此$\times 3$倍距离意味着$\div 9$倍作用力。
Many charges add as vectors
- With several charges, find the force from each one on its own.
- Then add those forces as vectors — the superposition 叠加 principle.
- $\vec F_{\text{net}} = \sum \vec F_i$, added tip-to-tail.
- This lets us build the force from any arrangement of charge.
多个电荷按矢量相加
- 有几个电荷时,先分别求出每一个产生的力。
- 然后把这些力按矢量相加——这就是叠加原理。
- $\vec F_{\text{net}} = \sum \vec F_i$,首尾相接地相加。
- 这样我们就能求出任意电荷排布产生的合力。
Select all · 所有 true statements about the electric force. · 选择关于电场力的所有正确陈述。
Coulomb's law is inverse-square, along the join, and superposes. It attracts OR repels. · 库仑定律是平方反比的、沿连线方向的、且满足叠加原理。它表现为吸引或排斥。
Two $+2\ \mu\text{C}$ charges sit $3\ \text{cm}$ apart. Find the force between them.
- $F = \dfrac{k\,q_1 q_2}{r^2} = \dfrac{(8.99\times10^9)(2\times10^{-6})^2}{(0.03)^2}$.
- $F \approx 40\ \text{N}$, and it is repulsive because both charges are positive.
两个 $+2\ \mu\text{C}$ 的电荷相距 $3\ \text{cm}$。求它们之间的力。
- $F = \dfrac{k\,q_1 q_2}{r^2} = \dfrac{(8.99\times10^9)(2\times10^{-6})^2}{(0.03)^2}$。
- $F \approx 40\ \text{N}$,而且是排斥的,因为两个电荷都是正的。
Put the magnitudes of the charges into $F = k q_1 q_2 / r^2$, then decide the direction separately: repel for same signs, attract for opposite. Don't let a stray minus sign from a negative charge flip your force arrow the wrong way.
把电荷的大小代入 $F = k q_1 q_2 / r^2$,再单独判断方向:同号相斥,异号相吸。不要让负电荷的负号把你的力箭头指错方向。
The electric force between two point charges obeys Coulomb's law $F = \dfrac{k\,q_1 q_2}{r^2}$ — an inverse-square law. Like charges repel, opposite charges attract, and the forces from many charges add as vectors (superposition).
两个点电荷之间的电力遵循库仑定律 $F = \dfrac{k\,q_1 q_2}{r^2}$——一条平方反比定律。同种电荷相斥,异种电荷相吸,而多个电荷产生的力按矢量相加(叠加)。