Electric fields · 电场
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| electric field/ɪˈlektrɪk fiːld/ | 电场 | diàn chǎng |
| electric field strength/ɪˈlektrɪk fiːld streŋθ/ | 电场强度 | diàn chǎng qiáng dù |
| field line/fiːld laɪn/ | 场线 | chǎng xiàn |
| test charge/test tʃɑːdʒ/ | 检验电荷 | jiǎn yàn diàn hè |
| vector/ˈvektə/ | 矢量 | shǐliàng |
| negative charge/ˈneɡətɪv tʃɑːdʒ/ | 负电荷 | fù diàn hè |
| point charge/pɔɪnt tʃɑːdʒ/ | 点电荷 | diǎn diàn hè |
| dipole/ˈdaɪpəʊl/ | 偶极子 | ǒu jí zi |
| uniform field/ˈjuːnɪfɔːm fiːld/ | 匀强场 | yún qiáng chǎng |
A force with nothing in between
- Rub a comb on your hair and hold it over torn paper. The paper jumps up to meet it, across a gap of air, with nothing touching.
- Newton called action at a distance across empty space philosophically unacceptable, and he was right to be uneasy. The modern answer is that the comb changes the space around it, and the paper responds to the space it is in.
- That altered region is an electric field 电场, and the whole of this topic is a way of describing it precisely enough to calculate with.
- This lesson is the definition of electric field strength 电场强度, the force it produces, and how field lines 场线 represent it.
中间什么也没有的一个力
- 把梳子在头发上蹭一蹭,举到碎纸片上方。纸片穿过一段空气跳上去迎接它,中间什么都没有接触。
- 牛顿认为跨越真空的超距作用在哲学上不可接受,而他有理由不安。现代的答案是:梳子改变了它周围的空间,而纸片是对它所处的空间作出反应。
- 那个被改变的区域就是电场(electric field),而整个单元就是一种把它描述得足够精确、可以拿来计算的办法。
- 这一课讲电场强度(electric field strength)的定义、它产生的力,以及场线(field lines)怎样表示它。
Field strength
- The electric field strength at a point is the force per unit positive charge acting on a small test charge 检验电荷 placed at that point:
- Three words carry the two marks. Force per unit charge, not "force on a charge". Positive, which is what fixes the direction. And small or test, so the charge does not disturb the field it is measuring.
- The unit is $\text{N/C}$, which is the same as $\text{V/m}$. $E$ is a vector 矢量.
场强
- 某点的电场强度是放在该点的小检验电荷(test charge)所受的单位正电荷所受的力:
- 三个词承载着两分。单位电荷所受的力,而不是"电荷所受的力"。正,这是确定方向的关键。以及小或检验,这样电荷才不会扰动它所测量的场。
- 单位是 $\text{N/C}$,与 $\text{V/m}$ 相同。$E$ 是矢量(vector)。
Electric field strength is the force per unit: · 电场强度是每单位什么上的力:
$E = \dfrac{F}{q}$ — the force on each coulomb of a small positive test charge. · $E = \dfrac{F}{q}$——作用在一个小正检验电荷每库仑上的力。
A charge of $2.0\ \text{C}$ feels a force of $6.0\ \text{N}$. What is the field strength? · 一个 $2.0\ \text{C}$ 的电荷受到 $6.0\ \text{N}$ 的力。场强是多少?
$E = \dfrac{F}{q} = \dfrac{6.0}{2.0} = 3.0\ \dfrac{\text{N}}{\text{C}}$. · $E = \dfrac{F}{q} = \dfrac{6.0}{2.0} = 3.0\ \dfrac{\text{N}}{\text{C}}$。
Which words are needed in the two-mark definition of electric field strength? Select all · 所有 that apply. · 电场强度的两分定义需要哪些词?选出所有适用的。
A moving charge feels the same electric force. The three marked ideas are per unit charge, positive, and a small test charge. · 运动电荷受到的电场力是一样的。要评分的三个意思是:单位电荷、正,以及小的检验电荷。
The force on a charge
- Rearranged, the field tells you the force on any charge placed in it:
- A positive charge is pushed along the field. A negative charge 负电荷 is pushed against it, since $q$ is negative.
- In these problems gravity is almost always negligible. An electron in a field of $1500\ \text{V/m}$ accelerates at $2.6 \times 10^{14}\ \text{m/s}^2$, against $9.81$ from gravity, so the weight is ignored unless the question is specifically about balancing it.
A field strong enough to tear electrons off air molecules
电荷所受的力
- 移项后,场就告诉你放进其中的任何电荷所受的力:
- 正电荷被顺着场推。负电荷(negative charge)被逆着场推,因为 $q$ 为负。
- 这类问题中引力几乎总可忽略。电子在 $1500\ \text{V/m}$ 的场中加速度为 $2.6 \times 10^{14}\ \text{m/s}^2$,而引力只给 $9.81$,所以除非题目专门问平衡重力,否则重力忽略不计。
强到能把电子从空气分子上撕下来的场
The force on a negative charge is opposite to the field direction. · 负电荷受到的力与场的方向相反。
Field direction is defined for a positive charge; a negative charge feels the opposite force. · 场的方向是为正电荷定义的;负电荷受到相反的力。
Worked example: field from an acceleration
- A proton accelerates at $2.00\ \text{m/s}^2$ in an electric field, with no other force acting. Find the field strength. ($m_{\text{p}} = 1.67 \times 10^{-27}\ \text{kg}$, $e = 1.60 \times 10^{-19}\ \text{C}$.)
- The electric force is the only force, so $qE = ma$.
- Run the same rearrangement the other way for the acceleration of an electron in a given field: $a = eE/m_{\text{e}}$, which is enormous because the electron's mass is so small.
例题:由加速度求场强
- 一个质子在电场中以 $2.00\ \text{m/s}^2$ 加速,没有其他力作用。求场强。($m_{\text{p}} = 1.67 \times 10^{-27}\ \text{kg}$,$e = 1.60 \times 10^{-19}\ \text{C}$。)
- 电场力是唯一的力,所以 $qE = ma$。
- 同样的移项反过来用,可求电子在给定场中的加速度:$a = eE/m_{\text{e}}$,数值极大,因为电子的质量太小。
A proton (mass 1.67e-27 kg, charge 1.60e-19 C) accelerates at 2.00 m/s^2 in an electric field alone. What is the field strength, in units of 10^-8 V/m? · 一个质子(质量 1.67e-27 kg,电荷 1.60e-19 C)仅在电场中以 2.00 m/s^2 加速。场强是多少,以 10^-8 V/m 为单位?
The electric force is the only force, so qE = ma and E = ma/q = 2.09e-8 V/m. The same rearrangement gives an electron's acceleration in a known field. · 电场力是唯一的力,所以 qE = ma,E = ma/q = 2.09e-8 V/m。同样的移项可求电子在已知场中的加速度。
Field lines
- A field line shows, by its direction, the direction of the force on a positive charge placed there, and by its spacing, the strength of the field: closer lines mean a stronger field.
- Lines start on positive charges and end on negative ones, or run to infinity. They never cross, since the force at a point has one direction.
- Every line carries an arrow, and lines meet the surface of a conductor at right angles.
- A sketch is marked on exactly those points: arrows drawn, lines not crossing, correct starts and ends, and sensible spacing.
Four standard patterns worth being able to draw from memory
场线
- 场线用它的方向表示放在那里的正电荷所受力的方向,用它的疏密表示场的强弱:线越密场越强。
- 线从正电荷出发、终止于负电荷,或者伸向无穷远。它们绝不相交,因为一点处的力只有一个方向。
- 每条线都带箭头,而且线与导体表面垂直相交。
- 作图题正是按这几点评分:画了箭头、线不相交、起止正确、疏密合理。
四种值得能凭记忆画出来的标准图样
The patterns to know
- A positive point charge 点电荷: radial lines pointing outwards. A negative one: radial lines pointing inwards.
- Two opposite charges, a dipole 偶极子: lines curving from the positive to the negative.
- Two parallel charged plates: equally spaced parallel lines, a uniform field 匀强场, apart from the curvature at the edges.
要会的图样
- 正点电荷(point charge):向外的辐射状直线。负点电荷:向内的辐射状直线。
- 两个异号电荷,即偶极子(dipole):从正弯向负的曲线。
- 两块平行带电板:等间距的平行直线,即匀强场(uniform field),边缘弯曲处除外。
Electric fields · 电场
E ∝ Q / r²
A charge sets up a radial field — out for +, in for −, obeying the inverse-square law. · 一个电荷建立一个径向场——正电荷向外,负电荷向内,服从 平方反比定律。
Electric field lines: · 电场线:
They run from + to −, never cross, and are closer where the field is stronger. · 它们从 + 到 −,从不相交,在场更强处更密。
Field lines drawn closer together mean a ____ field. · 画得更密的场线表示一个 ____ 的场。
Line spacing shows the strength — closer lines, stronger field. · 场线的间距表示强度——线越密,场越强。
Which are true of electric field lines? Select all · 所有 that apply. · 关于电场线,哪些是对的?选出所有适用的。
A field line shows the direction of the force, not the trajectory: a charge entering sideways follows a curve that crosses the lines. · 场线表示力的方向,不是轨迹:侧向进入的电荷走的曲线会穿过这些线。
A charged conducting sphere
- Charge on an isolated conductor sits on its outer surface, spread evenly if the sphere is alone.
- Outside, the field lines are radial and evenly spaced: exactly the pattern of a point charge at the centre, so $r$ is measured from the centre.
- Inside a hollow or solid conductor the field is zero, and the conductor is therefore an equipotential.
- On an $E$ against $x$ graph for such a sphere, the radius is where $E$ jumps up from zero, and the charge follows from any point on the curve using $Q = 4\pi\varepsilon_0 r^2 E$.
带电导体球
- 孤立导体上的电荷位于它的外表面,球单独存在时均匀分布。
- 在外部,场线是辐射状且等间距的:恰好是位于球心的点电荷的图样,所以 $r$ 从球心量起。
- 空心或实心导体内部场为零,因而该导体是一个等势体。
- 在这种球的 $E$ 对 $x$ 图上,半径就是 $E$ 从零跳起来的位置,而电荷可由曲线上任一点用 $Q = 4\pi\varepsilon_0 r^2 E$ 求出。
Marks that slip away
- The definition is force per unit positive charge on a small test charge. All three ideas are marked.
- Field lines never cross and always carry an arrow. A sketch without arrows scores nothing.
- Inside a conductor the field is zero, and outside it behaves as a point charge at the centre.
- Gravity is negligible for a charged particle in a field unless the question is about balancing weight, as with an oil drop.
容易丢掉的分
- 定义是小检验电荷上单位正电荷所受的力。这三个意思都要评分。
- 场线绝不相交,而且总带箭头。没有箭头的图不得分。
- 导体内部场为零,而在外部它表现得像位于球心的点电荷。
- 除非题目问的是平衡重力(比如油滴),否则场中带电粒子的引力可忽略。
What is the electric field inside a hollow charged conducting sphere? · 空心带电导体球内部的电场是多少?
The fields of all the surface charges cancel inside, so the conductor is an equipotential. Outside it behaves as a point charge at the centre. · 内部所有表面电荷的场相互抵消,所以导体是等势体。在外部它表现为位于球心的点电荷。
You've got it
- electric field strength is the force per unit positive charge on a small test charge: $E = F/q$, a vector in $\text{N/C}$ or $\text{V/m}$
- $F = qE$: positive charges are pushed along the field, negative ones against it, and gravity is normally negligible
- field lines show direction by their arrows and strength by their spacing; they start on positive, end on negative, never cross, and meet conductors at right angles
- a charged sphere behaves outside as a point charge at its centre, and the field inside a conductor is zero
你掌握了
- 电场强度是小检验电荷上单位正电荷所受的力:$E = F/q$,是矢量,单位 $\text{N/C}$ 或 $\text{V/m}$
- $F = qE$:正电荷被顺着场推、负电荷被逆着场推,而引力通常可忽略
- 场线用箭头表示方向、用疏密表示强弱;起于正、止于负,绝不相交,并与导体垂直相交
- 带电球在外部表现为位于球心的点电荷,而导体内部的场为零