Electric Fields · 电场
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| field/fiːld/ | 场 | chǎng |
| electric field/ɪˈlektrɪk fiːld/ | 电场 | diàn chǎng |
| test charge/test tʃɑːdʒ/ | 检验电荷 | jiǎn yàn diàn hè |
| uniform/ˈjuːnɪfɔːm/ | 均匀 | jūn yún |
How does one charge feel another across empty space?
- A charge pushes another far away, with nothing visibly between them.
- We explain it with a field 场: charge fills the space around it with influence.
- Any other charge placed there feels a force from the local field.
- The field is the middle-man that carries the electric force.
一个电荷如何隔着空旷的空间感受另一个?
- 一个电荷推动远处的另一个,中间看不见任何东西。
- 我们用场来解释:电荷把影响充满它周围的空间。
- 放在那里的任何其他电荷都会感受到当地场的力。
- 场就是传递电力的中间人。
Field = force per unit charge
- The electric field 电场 at a point is the force a $+1\ \text{C}$ test charge 检验电荷 would feel there.
- $\vec E = \dfrac{\vec F}{q}$, measured in newtons per coulomb (N/C).
- $E$ is a vector: it has a direction at every point.
- Once you know $E$, the force on any charge is just $\vec F = q\vec E$.
场 = 单位电荷受的力
- 某点的电场,就是一个 $+1\ \text{C}$ 的试探电荷放在那里会受到的力。
- $\vec E = \dfrac{\vec F}{q}$,单位是牛每库仑(N/C)。
- $E$ 是矢量:每一点都有方向。
- 一旦知道 $E$,任何电荷受的力就是 $\vec F = q\vec E$。
The electric field at a point is the: · 某点的电场强度是该点的：
$\vec E = \vec F / q$ — the force a unit positive charge would feel. · $\vec E = \vec F / q$ — 单位正电荷将感受到的力。
Once you know the field $E$, the force on a charge $q$ is $F =$ ____. · 一旦知道电场$E$，电荷$q$所受的力就是$F =$ ____。
$\vec F = q\vec E$ — multiply the field by the charge. · $\vec F = q\vec E$——将电场乘以电荷量。
The field of a point charge
- A point charge $Q$ makes a field $E = \dfrac{kQ}{r^2}$ at distance $r$.
- It points away from a positive $Q$ and toward a negative $Q$.
- It is strongest near the charge and fades as $1/r^2$.
- Field lines show the direction; where they crowd, the field is stronger.
点电荷的场
- 一个点电荷 $Q$ 在距离 $r$ 处产生场 $E = \dfrac{kQ}{r^2}$。
- 它从正 $Q$ 指向外,朝负 $Q$ 指向内。
- 它在电荷附近最强,并随 $1/r^2$ 减弱。
- 电场线显示方向;线越密,场越强。
Map a charge's field · 绘制电荷的电场图
Change the sign and size of the charge and watch how its field lines rearrange. · 改变电荷的符号和大小，观察其电场线如何重新排列。
Find the field (in N/C) $3\ \text{m}$ from a $+6\ \text{nC}$ charge. Use $k = 9\times10^9$. · 求距$3\ \text{m}$处$+6\ \text{nC}$电荷产生的电场（单位：N/C）。使用$k = 9\times10^9$。
$E = \dfrac{(9\times10^9)(6\times10^{-9})}{3^2} = \dfrac{54}{9} = 6\ \text{N/C}$.
Reading field lines
- Lines start on positive charge and end on negative charge.
- They never cross — the field has one direction at each point.
- Closer lines mean a stronger field.
- The line's tangent gives the direction of $\vec E$ (and the force on a $+$ charge).
读电场线
- 线起于正电荷,止于负电荷。
- 它们从不相交——每一点场只有一个方向。
- 线越近,场越强。
- 线的切线给出 $\vec E$ 的方向(也是 $+$ 电荷受力的方向)。
Two electric field lines can cross at a point. · 两条电场线可以在某点相交。
Lines never cross — the field has only one direction at each point. · 电场线永不相交——每一点只有一个电场方向。
Select all · 所有 true statements about field lines. · 选择关于电场线的所有正确陈述。
Lines run + to −, crowd where strong, and never cross. · 电场线从+指向-，密集处场强，永不相交。
A uniform field
- Between two large parallel plates the field is uniform 均匀 — same everywhere.
- The lines are straight, evenly spaced, and point from $+$ to $-$.
- A uniform field gives a constant force, so a charge moves like a projectile.
- We will use this constant-field picture for capacitors.
均匀场
- 在两块大平行板之间,场是均匀的——处处相同。
- 电场线笔直、等间距,从 $+$ 指向 $-$。
- 均匀场给出恒定的力,所以电荷像抛体一样运动。
- 我们将用这个恒场图像来研究电容器。
Between two large parallel plates the field is: · 两块大平行板之间的电场是：
Parallel plates make a uniform field: straight, evenly spaced lines. · 平行板产生均匀电场：直线且间距相等。
Find the field $2\ \text{cm}$ from a $+5\ \text{nC}$ charge. Use $k = 9\times10^9$.
- $E = \dfrac{kQ}{r^2} = \dfrac{(9\times10^9)(5\times10^{-9})}{(0.02)^2}$.
- $E \approx 1.1\times10^{5}\ \text{N/C}$, pointing away from the charge.
求距一个 $+5\ \text{nC}$ 电荷 $2\ \text{cm}$ 处的场。取 $k = 9\times10^9$。
- $E = \dfrac{kQ}{r^2} = \dfrac{(9\times10^9)(5\times10^{-9})}{(0.02)^2}$。
- $E \approx 1.1\times10^{5}\ \text{N/C}$,方向背离电荷。
The field $\vec E$ exists whether or not a test charge is there — it is a property of space made by the source charge. Don't say "no charge, no field": the source still fills space with $E$.
场 $\vec E$ 无论有没有试探电荷都存在——它是源电荷赋予空间的性质。别说"没有电荷就没有场":源仍然用 $E$ 充满空间。
The electric field is the force per unit charge, $\vec E = \vec F / q$ (N/C), a vector pointing away from $+$ and toward $-$. A point charge makes $E = kQ/r^2$; field lines show its direction, and closer lines mean a stronger field.
电场是单位电荷受的力,$\vec E = \vec F / q$(N/C),一个从 $+$ 指向外、朝 $-$ 指向内的矢量。点电荷产生 $E = kQ/r^2$;电场线显示方向,线越近场越强。