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电的实际工作原理

How Electricity Actually Works

I made a video about a gigantic circuit
我曾制作了一个巨型电路相关的视频
with light-second long wires that connect up to a light bulb,
该电路用1光秒长的电线连接着1个灯泡
which is just one meter away from the battery and switch,
从电池到开关仅有1米长
and I asked you, after I closed the switch,
现在我问你 开关闭合之后
how long will it take for us to get light from that light bulb?
灯泡亮起需要多长时间?
And my answer was 1/c seconds.
我的答案是3亿分之1秒
And his answer is wrong!
他的答案是错误的!
We would be able to communicate faster than the speed of light!
我们的通讯速度将会比光速还快!
That violates causality and common sense.
这有悖于因果关系和常识
This is actually a bit misleading.
这实际上有点误导
Misleading.
误导
Misleading in a way.
某种意义上误导了
Extremely unconvinced.
太难以令人信服了
Naughty Mr. Veritasium has stirred up a right hornet’s nest.
调皮的真理先生捅了马蜂窝了
Clearly I did not do a good job of explaining what was really going on in the last video.
很显然上个视频中发生的事 我解释得不太清楚
So I wanna clear up any confusion that I created.
所以我想澄清一下这些我所制造的困惑
So behind me, we have a scaled down model of this circuit.
在我身后 是按该电路的等比缩小的模型
It is only 10 meters in length on either side.
两边仅有10米长
Obviously that’s a lot shorter than one light-second,
显然 比1光秒短很多
but for the first 30 nanoseconds,
但是对于第1个30纳秒而言
this model should be identical to the big circuit,
这个模型与该巨型电路是相同的
and Caltech has very fast scopes,
加州理工学院有高速示波器
so we’ll be able to see what’s going on in this time.
所以我们将会弄明白这次的实验
I got a ton of help on this from Richard Abbott,
Richard Abbott 给了我很多帮助
who works on LIGO, the gravitational wave detector.
他在引力波探测天文台LIGO工作
Over here, we are going to put a little resistor,
在这里我们要加一个小电阻
which is gonna be the stand in for our light bulb
作为灯泡的替代物
and we’re going to measure it with a scope and see essentially,
然后我们将用一个仪器进行测量
what is the time delay between applying a pulse
看看在电路的一边施加脉冲
on the other side, basically flicking the switch,
另一边仅是打开开关 电阻两端
for us to get a voltage across our resistor.
产生电压需要的时间到底是多久
And the magnitude of that voltage is really important.
该电压的强弱十分重要
A lot of people thought it would be negligible.
很多人觉得它无关紧要
The amount of energy supplied by this is so minuscule.
它提供的能量数值微不足道
A tiny, tiny effect, right?
只造成极小 极小的影响 对吗?
The amount of power you’re getting to the lamp over here, it’s nuff-all
这个大小的能量对此电灯来说足够了
He meant the light turns on
他的意思是 在任何电流强度下
at any current level immediately.
这个灯泡都会立刻亮起来
That is not what I meant.
我不是这个意思
Well, actually, with that assumption,
呃 实际上 在这种假设下
Derek’s answer is wrong.
Derek 的答案是错误的
The light never turns off no matter the state of the switch.
不论开关打开还是闭合 电灯一直没被关掉
Some electrons will jump the gap
有些电子可以跳过这个间隙
and result in an extremely small continuous leakage current.
然后产生一种极小的 持续的 泄漏电流
Let me be clear about what I am claiming.
让我清楚地解释一下我的观点
Okay, it is my claim that we will see voltage and current,
好 我的观点是我们将会看到
through the load that is many orders of magnitude greater than leakage current,
比泄漏电流大许多数量级的电压和电流 通过负载
an amount of power that would actually produce visible light,
这样大小的电流通过一个合适的装置
if you put it through an appropriate device.
它将会产生可见光
And we will see that power there in roughly the time
并且大概在电流通过这一米的间距所需时间之后
it takes the light to cross the one meter gap.
我们将会观察到发光现象
But to understand why this happens,
但是为了理解这事发生的原因
we first have to clear up some misconceptions
首先 我们要扫除我在评论中
that I saw in responses.
看到的一些错误观念
Misconception number one is thinking that electrons
错误观念一:认为电子
carry the energy from the battery to the bulb.
把电池中的能量带给灯泡
Let’s say we have a simple circuit with a battery and a bulb,
假设我们用一节电池和一颗灯泡做成了
operating at steady state.
一个运行稳定的简单电路
If you zoom in on the light bulb filament,
如果放大灯泡的灯丝
you’d see a lattice of positively charged cores of atoms.
你会看到带正电的原子核组成了晶格
The nucleus and lowest shells of electrons
这些原子核和最底层的电子
surrounded by a sea of negative electrons,
被海量的 可以在晶格内
which are free to move around the lattice.
自由移动的负电子包围着
The actual speed of these electrons is very fast,
这些电子的实际移动速度很快
around a million meters per second,
高达一百万米每秒
but all in random directions.
但移动的方向都是随机的
The average drift velocity of an electron
一个电子的平均漂移速度
is less than 0.1 millimeters per second.
小于0.1毫米每秒
Now frequently, an electron will bump into a metal ion,
电子漂移时常会碰撞金属离子
and transfer some or all of its kinetic energy to the lattice.
部分或全部动能会被转移到晶格中
The electron slows down and the metal lattice starts waggling more.
电子速度变缓 该金属晶格摆动开始增加
It heats up.
它的温度升高
And ultimately this is what causes the filament to glow and emit light.
最终导致灯丝慢慢发光发亮
So a lot of people will look at this and conclude
所以很多人看到此处会认为
the electron carried the energy from the battery to the bulb
电子携带电池的能量到达灯泡
where it dissipated its kinetic energy as heat,
并在此处把动能释放为热能
but consider, where did the electron get its kinetic energy
但是思考一下 在碰撞发生之前
from before the collision?
电子的动能来自哪里?
It didn’t carry that energy from the battery.
它携带的动能并非来自于电池
In fact, if the circuit has only been on for a short time,
事实上 如果此电路只是短时间通电
that electron hasn’t been anywhere near the battery.
那这点时间还不够电子漂移到电池的附近
So how was it accelerated before the collision?
因此 在碰撞之前 电子怎样加速呢?
The answer is, it was by an electric field in the wire.
答案是:靠电线内部的电场加速
The electron repeatedly collides with the lattice, and loses energy.
电子与晶格反复碰撞并丢失能量
And after each collision, it is again accelerated by the electric field.
每次碰撞后 电场再次给电子加速
So although it is the electron that transfers energy
因此 虽然是电子将能量转移到晶格
to the lattice, the energy came from the electric field.
但是 该能量却来自于电场
So where does that electric field come from?
那么电场又来自于哪里?
Well, a lot of animations make it look like the electrons
呃 很多动画制作得好像
push each other through the circuit via their mutual repulsion.
电子通过相互排斥 推动彼此通过电路
So you might think the electric field
所以 你可能会认为电场
comes from the electron behind it.
来自于它背后的电子
There is the analogy of water flowing through a hose,
类似于从水管流出的水
or marbles in a tube.
或者从管道滑出的弹珠
This is misconception two, thinking that
这是第二个错误观念
mobile electrons push each other through the circuit.
认为流动电子推动彼此通过电路
That is not how electrons flow in circuits.
这不是电子流过电路的方式
The truth is if you average over a few atoms,
事实是 如果按几个一组将原子平分
you find the charge density
你会发现导体内部
everywhere inside a conductor is zero.
任何地方的电荷密度都为0
The negative charge of electrons
电子的负电荷
and the positive cores of atoms perfectly cancel out.
和原子核的正电荷完美地抵消了
So for each repulsive force between electrons,
因此 对于电子之间的每一个斥力而言
there is an equal and opposite force
旁边的正离子对它有一个
from the positive ion next to it.
大小相等 方向相反的作用力
These forces cancel out.
这些力相互抵消
So mobile electrons cannot push each other through the wire.
所以流动电子不能推动彼此通过电线
So where does the electric field come from?
那么电场从何而来?
Misconception number three is that it comes entirely from the battery.
错误观念三 认为电场完全来自于电池
This makes intuitive sense,
从直觉上讲 这说得过去
since the battery is the active element in the circuit,
因为在电路中电池是有源元件
it has a positive side and a negative side.
它有一个正极和一个负极
So it has an electric field,
所以它会产生一个电场
But this is not the electric field
但此电场并不是那个
that all the electrons within the wire experience.
电线内所有电子都会经过的电场
Consider that the electric field
考虑到靠近电池的地方
of the battery is much larger close to the battery.
电池产生的电场会强得多
So if its field were really what’s pushing the electrons around,
因此 如果电子真是由电池的电场推动的
then if you brought the light bulb close to the battery,
那么如果让灯泡靠近这个电池
then the bulb would glow much brighter.
灯泡就会变亮许多
And it doesn’t.
然而并没有
The truth is that the electric field in the wire
事实是 电线中的电场
comes both from the battery and from charges
不仅来自于电池 也来自于
on the surface of the wires of the circuit.
该电路中 电线表面的电荷
As you go along the wire from the negative end of the battery to the positive end,
沿着电线 从电池的负极到它的正极
there is a gradient of charge built up on its surface,
电线的表面便会形成一个电荷梯度
starting with an excess of electrons,
开始时有大量的电子
through to roughly no charge in the middle,
直到中间几乎没有电荷
as we’ll see the steepest charge gradient is actually
正如我们所见 电荷梯度最大处 其实是
across the load to a deficiency of electrons,
横跨负载 通向电子缺乏端的地方
the exposed positive cores of atoms on the surface
那里 带正电的原子核
of the positive end of the wire.
位于电线带正电的末端表面
All these charges and the charges on the battery
所有的这些电荷以及电池的电荷
create the electric field everywhere inside the wires.
在电线内部 创造了无处不在的电场
They also create an electric field in the space around the wires.
它们也在电线周围的空间内 创造了电场
These surface charges were set up almost instantaneously
一旦把电池安装到电路中去
when the battery was inserted into the circuit.
就会立刻形成这些表面电荷
You might think you’d have to move electrons
你可能认为 电子必须移动很长的距离
a significant distance to create this charge distribution,
才能形成这样的电荷分布
but that is not the case.
但事实不是这样
Even a slight expansion or contraction of the electron sea,
即使是电子均匀地移动一个质子的半径的距离
with electrons moving on average, the radius of a proton,
造成的电子海的轻度扩张和收缩
can establish the surface charges you see.
都可以形成你所看见的表面电荷
So the time for the charges to move
所以电荷移动所花费的时间
is completely negligible.
完全可以忽略不计
The speed of the setup process is limited
表面电荷形成的速度
only by the speed of light.
只受光速的限制
Once that surface charge distribution has been established,
一旦表面电荷分布形成
the battery does continuous work to maintain it,
电池持续地逆着库仑力移动电子流过电池
by moving electrons through the battery against the Coulomb force.
来维持表面电荷的运行
In the load, the electric field
在负载灯泡内部
created by all the surface charges, accelerates electrons,
表面电荷创造了电场 电场加速电子移动
which dissipate their energy in collisions with the lattice.
加速的电子在碰撞中将能量转移给晶格
So the battery is putting energy into the field,
因此电池将能量释放到电场
which electrons take out and transfer to the load.
电子带出这些能量 并转移给负载灯泡
An electrical engineer who made a response video,
一位叫Ben Watson的电气工程师制作了一个回应视频
Ben Watson, came up with a good analogy.
他想出了一个很好的类比
The battery is like a shepherd.
电池就像牧羊人
The surface charges are the sheep dogs
表面电荷是牧羊犬
responding to his orders.
服从牧羊人的命令
And the mobile electrons are the sheep,
移动的电子是绵羊
guided by those barking dogs.
由那些吠犬引导
The surface charge description of electric circuits
大部分教科书中删去了
is omitted from most textbooks,
对于电路的表面电荷的描述
but there is a great treatment of it
但是Chabay 和Sherwood却在
in Matter and Interactions by Chabay and Sherwood.
《物质与相互作用》一书中着重描述了这个知识
They also have a VPython simulation where you can see
他们还建立了一个VPython仿真
the positive surface charge in red,
模型中 正极的表面电荷是红色的
and negative surface charge in blue.
负极的表面电荷是蓝色的
You can see how this entire charge distribution
你可以看到整个电荷分布是如何
creates a net electric field shown by the orange arrow,
在电路的内部和周围以及电线的内部
everywhere in and around the circuit,
创造一个 如橙色箭头所示的
everywhere inside the wire,
无处不在的净电场
The electric field has the same magnitude
该电场有相同的强度
and its direction is along the wire.
并且它的方向是顺着电线的
This is really showing you the electric field
这个模型真实地向你展示了
in the center of the wire, but it’s depicted on the surface
电线中心的电场 只不过它是画在表面的
so you can see it.
所以你可以看到它
In this circuit,
在这个电路中
all the conductors are made of the same material,
所有的导体都是由相同的材料做成的
but the segment at the bottom
但是下面这部分的
has a much narrower cross section.
通过路径更为狭小
So it represents a resistor.
所以这代表了一个电阻
Since the cross sectional area is smaller,
由于这个通过路径区更小
the electron drift velocity through the resistor
通过这个电阻时 电子的漂移速度
has to be higher so that it can carry the same current
必须要更快 这样才能与电路中
as everywhere else in the circuit.
其他地方一样 携带相同的电流
Now, drift velocity is directly proportional to electric field.
现在 漂移速度与电场成正比
So the electric field must be largest inside the resistor.
所以 电阻内部的电场一定是最大的
And this is achieved by having the steepest gradient
这种现象得以实现 是因为
of surface charges here.
这里的表面电荷的梯度最大
You can also see the contribution to the net electric field
你也可以看到 紫红色箭头
from the battery in magenta,
代表电池带来的电场
and the contribution from surface charges in green.
绿色箭头代表表面电荷带来的电场
Far from the battery,
在远离电池的地方
most of the electric field is due to surface charges,
大部分的电场是表面电荷带来的
whereas close to the battery, it has a greater contribution
而电池的近端 电池带来的电场占比更大
and the field due to surface charges
并且表面电荷产生的电场
is actually in the opposite direction
实际上与电池产生的电场
to the field from the battery.
方向相反
So to sum up, electrons don’t carry the energy
总得来说 电子既没有从电池处
from battery to bulb,
携带能量到灯泡
nor do they push each other through the wire.
也没有推动彼此通过电线
They are pushed along by an electric field,
电池的电荷产生的电场
which is created by charges on the battery,
以及电线的表面电荷产生的电场
and charges on the surface of the wires.
推动着它们前进
With this view of circuits,
带着这种观点看电路
things that might have previously seemed mysterious,
原本似乎很离奇的事情
make a lot more sense.
就解释得通了
Like if electrons leave a battery at the same rate,
比如 如果电子离开电池
and with the same drift velocity as they return,
和回流的时候速度一样
how do they carry energy from the battery?
那么 它们怎么从电池带走能量?
The answer is they don’t.
答案是 它们没有带走能量
They are accelerated by the electric field
在电子与晶格发生每次碰撞之前
before each collision with the lattice.
电场会给电子加速
At a junction, how do the correct number of electrons
在结点处 电子是怎样以正确的数量
go down each path?
通过每条路径?
Well, they’re guided by the electric field, which extends everywhere throughout the circuit.
呃 它们被处处存在的电场引导着
The fields are the main actors,
电场才是主要因素
extending everywhere throughout the circuit,
它们遍及电路的每个角落
and the electrons are just their pawns.
而电子只是它们的小兵
So how does this apply to the big circuit?
所以这是如何作用于那个大电路的呢?
When the battery is connected into the circuit,
当把电池连入到电路时
even with the switch open, charges rearrange themselves.
即使开关没有闭合 电荷也会自动重新分布
On the negative side of the battery,
在电池的负极
there is an excess of electrons
电线和开关的表面
on the surfaces of the wires and the switch.
有大量的电子
On the positive side, there is a deficiency of electrons.
而正极缺少电子
So positive charges built up on the surface of the wires.
所以正电荷分布在电线的表面
The charges rearrange themselves until the electric field
电荷自动重新分布 直到
is zero everywhere inside the conductor.
导体内部所有地方的电场都为0
This electric field is due to all the surface charges
电场由所有表面电荷产生
and the charges on the battery.
以及电池的电荷
There is an electric field outside the wires
这些电荷使得电线外部形成一个电场
due to these charges, but it’s zero inside the wires.
但是电线内部的电场为0
We now have the full potential difference
现在我们知道了电池通过开关
of the battery across the switch.
形成了全电势差
And no current is full flowing, except for leakage current,
除了泄漏电流 完全没有电流能够流通
which I’ll assume is negligible.
而我假设泄漏电流是可以忽略不计的
When we close the switch,
当开关闭合时
the surface charges on both sides of the switch
开关两边的表面电荷
neutralize each other on contact.
在接触时会彼此抵消
And at that instant,
在那一瞬间
the electric field inside the conductor is no longer zero,
导体内部的电场不再为0
and current starts flowing through the switch.
电流开始流过开关
Simultaneously, the new electric field from the modified surface charges
同时 改变后的表面电荷产生的新的电场
radiates outwards at essentially the speed of light.
基本上以光速向四周辐射
And when it reaches the bulb,
当它辐射至灯泡时
the electric field inside it is no longer zero.
灯泡内部的电场就不再为0
So current starts to flow here too.
因此电流也开始在此处流通
This is why I said the bulb lights up in 1/c seconds,
这就是我说灯泡亮起需要3亿分之1秒的原因
because the bulb was one meter from the switch,
因为灯泡离开关有1米
and the change in the electric field travels out at the speed of light.
并且电场的变化以光速向外传播
As some of you pointed out,
正如一些人指出的那样
the answer should have been one meter divided by C.
答案本应该是1米除以光速
And I apologize for the casual use of units.
我很抱歉单位上用得比较随意
If you were to move the switch,
如果移动这个开关
then the bulb would take
那么这个灯泡亮起
a different amount of time to emit light,
需要的时间将会变得不一样
which just depends on the distance
这个时间取决于
between the switch and the bulb.
开关和灯泡的距离
In response to my original video,
为了回应我的原始视频
Ben Watson simulated a model of the circuit
Ben Watson用Ansys的一款叫做HFSS的软件
using software from Ansys called HFSS.
给这个电路建模
It provides a complete solution to Maxwell’s equations in three dimensions.
它给出了三维麦克斯韦方程的完全解
Now I have worked with Ben and Ansys
现在我与Ben合作 利用Ansys软件
to make these simulations.
制作出这些仿真
When the switch is closed,
当此开关闭合
you can see the electric field radiate out,
你可以看到这个电场向外辐射
and as it hits the far wire, it generates current.
当它到达远处的电线 就产生电流
The electric field is to the right.
电场方向向右
So the electrons flow to the left.
所以电子流向左边
This simulation shows the magnitude of the magnetic field,
这个模型展示了磁场的大小
which falls off pretty rapidly as it crosses the gap.
当通过这个间隙时 该磁场衰退得非常快
But then a magnetic field appears around the far wire,
但随后在远处的电线出现了一个磁场
and this magnetic field is created by the current in that wire.
该磁场是由电线中的电流产生的
To me, this suggests that it really is the electric field,
这就让我想到 其实是电场
and not the changing magnetic field
而不是这个正在变化的磁场
that creates the current through the load.
创造了通过负载的电流
Some commenters on the original video
原视频底下有人评论说
claimed my answer of three or four nanoseconds
我的答案 3到4纳秒
violates causality.
违背了因果关系
I guess they were thinking that the bulb
我猜他们认为
would only go on if the circuit were complete.
只有电路接通 灯泡才会亮起
And it wouldn’t if the circuit were broken somewhere,
而如果电路在半光秒内的某处断开
which could be up to half a light second away.
灯泡就不会亮
So it seemed like I was saying,
所以这就像是我在说
we could get information about the status
即使在半光秒开外的地方
of the whole circuit, even half a light second away,
仅需几纳秒 我们就可以得到
in just nanosecond seconds.
关于整个电路状态的信息
But that is not what I was saying.
但我不是这个意思
What I should have stated explicitly,
我本应清楚地表明
is that the bulb goes on
不论电路是否接通
regardless of whether the circuit is complete or not.
该灯泡都会亮起
The current flows through the load
电流流过负载灯泡
due to the electric field it experiences.
是因为它处在电场中
To illustrate this, Ben added a wire below the circuit
为证明这点 Ben在该电路下增加了一条电线
that is completely disconnected from it.
这条电线与该电路完全没有连接
You can see is that its response
你可以看见下面这条电线
to the changing electric field is virtually identical
对这个正在改变的电场的反应
to that of the top wire,
与上面的电线几乎完全相同
at least up until the signal reaches the far end
至少一直上升 直到该信号到达远端
and reflects back.
并反射回来
This is why my answer doesn’t break causality.
这就是我的答案没有违背因果关系的原因
At least initially, connected and disconnected wires
至少开始时 已经接通的电线和
behave exactly the same.
没有接通的电线的表现完全相同
Using this software,
使用这个软件
you can also simulate the Poynting vector
你也可以模拟坡印廷矢量
that is the cross product of electric and magnetic fields.
即电磁场的叉积
In the last video, I showed how the Poynting vector
在上个视频中 我展示了坡印廷矢量
indicates the direction of energy flow.
是如何指示能量流动的方向的
And after the switch is closed,
开关闭合后 不论另一根电线
the Poynting vector points out of the battery,
是否接通 坡印廷矢量都会穿过这个间隙
across the gap to the other wire, whether connected or not,
指向电池之外 到达另一条电线
because energy is carried by fields and not electrons,
因为能量是由电场 而不是电子携带的
it can go straight across the gap.
所以能量可以直接穿过这个间隙
So you might ask, why do we need wires at all?
你可能会问 那为什么我们仍然需要电线呢?
Well, we don’t, I mean, phones and toothbrushes
呃 不需要 我的意思是手机和牙刷
charge without wires connecting them
在没有电线连接输入电子流的情况下
to a stream of electrons,
仍然可以充电
and researchers have demonstrated remote charging
并且有研究表明 使用来自WiFi信号的能量
using the energy from WiFi signals.
也可以远程充电
Wires are more efficient because they channel the fields
电线效率更高是因为它们可以引导电场
and hence the energy from source to load.
因此能量可以从电源到达负载
Here’s another angle on the Poynting vector.
从另一个角度看坡印廷矢量
And you can see once there is current in the top wire,
你可以看见 只要上面的电线内有电流
the fields around it carry energy in both directions.
它周围的场从两个方向带走能量
Now, of course, the Poynting vector also points
现在 当然 正如大多数人期待的那样
parallel to the first wire,
坡印廷矢量
carrying the energy around the circuit
指向与第一根电线平行的方向
as most people would expect.
携带能量绕着电路走
But again, note how the energy is carried outside the wires,
但是再说一遍:注意能量是怎样被带出电线的
not in the wires.
而不是局限于电线内
Now admittedly, thinking about circuits this way
现在不可否认 这种看待电路的方式
is complicated.
是复杂的
And since nobody wants to solve Maxwell’s equations
仅仅是为了分析一个基本的电路
in three dimensions just to analyze a basic circuit,
没人愿意用三维麦克斯韦方程组解决
scientists and engineers have worked out shortcuts.
科学家和工程师想出了简便方法
For example, Ohm’s law,
例如 欧姆定律
voltage equals current times resistance,
电压等于电流乘以电阻
is just the macroscopic result of all the surface charges,
仅仅是所有的表面电荷
their electric fields and zillions of electrons
它们的电场以及无数的电子
bumping into zillions of metal ions.
与无数金属离子间碰撞的宏观结果
You can simplify all that physics
你可以把所有那些物理元素
into a single circuit element, a resistor,
简单归结为一个单一的电路元件 电阻
and the basic quantities of current and voltage.
以及基本量 电流和电压
This is called the lumped element model,
这就是所谓的集总元件模型
lump all the spread-out multi particle and field
把所有分散多质点和场的交互作用
interactions into a few discrete circuit elements.
归并为少量的离散电路元件
And we use this technique
每次我们画电路图时
every time we draw a circuit diagram.
都会使用这个技巧
So our original diagram of the big circuit is flawed
因此该大电路的原始电路图是有缺陷的
because fields between the wires are important to the problem,
因为电线间的场对这个问题也很重要
but there are no circuit elements to indicate these interactions.
但是没有电器元件指出这些交互作用
To fix it, we need to add capacitors all down the wires.
为了修正它 我们需要沿着电线添加电容器
These capture the effect charges on one wire
这些电容器能够捕获一条电线的电荷
have on the other.
对另一条电线的影响
If there are negative charges on the surface of the bottom wire, for example,
例如 如果下面这条电线的表面电荷为负
they’ll induce positive charges on the surface of the top wire.
那它们会在上面这条电线的表面产生正电荷
Also, since these wires are long,
并且 由于这些电线太长了
they’re gonna create significant magnetic fields
所以在它们周围将会产生显著的磁场
around them, which resist changes in current.
这些磁场能让电流保持不变
So we model this with inductors all the way down the wires.
所以我们沿着电线用电感模拟了该现象
We could also add resistors,
我们本来也可以加入一些电阻
making what electrical engineers would recognize
建立一个电气工程师所说的
as the distributed element model for a transmission line.
“输电线路的分布式元件模型”
But we’re assuming that these wires are super conducting.
但让我们假设这些是超导电线
So this is how we could model
所以我们是这样模拟
a super conducting transmission line.
一条超导输电电路的
This diagram offers another way of understanding
这个电路图提供了另外一种
why current flows through the load almost immediately.
理解为什么电流能立刻流入负载的方式
When you first apply a voltage across a capacitor,
当你第一次给一个电容器施加电压时
current flows as opposite charge builds up
由于两个极板产生了相反的电荷
on the two plates.
电流得以流动
In the short time limit, a capacitor is a short circuit.
在有限的短时间内 一个电容器就是一个短电路
It acts just like an ordinary wire.
它表现得就像一根平常的电线
Once it’s charged up, no more current flows,
一旦电容充满了 电流就不再流过
but by this point, the next capacitor is charging up.
这个时候 下一个电容器正在充电
And then the next one, and then the next one.
然后是下一个 再下一个
And so we have a loop of current that is expanding out
这就形成了一个大约以光速
at roughly the speed of light.
向外扩展的电流环路
This is of course, just another way of talking
当然 这只是用另外一种方式来讨论
about the effect the electric field
下面这条电线的电场
from the bottom wire has on the top wire.
对上面这条电线的影响
One reason it’s useful to look at the circuit this way,
用这种方式看待这个电路是有效的
is because you can use the values of inductance
一个理由是 你可以利用电感值和电容值
and capacitance to calculate the characteristic impedance of the transmission lines.
来计算这些输电线路的特性阻抗
You can think of this as the resistance
你可以把特性阻抗 看作
to alternating current that a source would see
电源向电线发送信号时
when sending a signal down the wires.
对交流电产生的阻碍作用
The characteristic impedance is equal to the square root
该特性阻抗等于
of inductance divided by capacitance.
电感除以电容之商的平方根
And for our circuit,
对于我们这里的电路而言
I measured the capacitance and the inductance of the lines,
我测量了线路的电容和电感
11.85, call it, microhenrys.
11.85 单位 微亨
So we got a characteristic impedance of about 550 Ohms.
所以特性阻抗大约是550欧姆
To maximize the power delivered to our load,
为了求出传输给负载的能量的最大值
we want its resistance to equal the sum of the other
我们让它的电阻等于该电路中
impedances in the circuit.
其他阻抗的总和
So that’s why we picked a 1.1 kilo-Ohm resistor.
所以我们才选择了一个1.1千欧的电阻
Now, I hope you’re convinced that current will flow
现在 我希望“电场一到达电线远端
as soon as the electric field reaches the far wire.
电流就会流动”这个道理已经说服了你
The question is, how much?
问题是 数量是多少呢?
Are we gonna see an appreciable voltage
即使这些线路只有一米远
even with these lines a meter apart?
我们也会测量到强大的电压吗?
That’s what it seemed like a lot of people were doubting in the last video.
在上个视频中很多人对此似乎有疑问
So that’s really what we want to find out here.
所以在这里我们真的想要找出答案
Okay, so now we’re putting a pulse in there.
好 现在我们会在这里施加一个脉冲
Yep.

Well looky, looky, Derek.
啊 看哪看哪 Derek
So what do we got that yellow one is our-
所以显示了什么 那个黄色的是?
Got a fraction of the applied voltage overshoot.
显示出外加电压过冲的一个片段
So it looks to me like the initial voltage
所以在我看来现在的原始电压
that we’re getting is about five volts per division.
大概每格电压值是5伏
So it looks like about five volts,
看起来大概是5伏
roughly four or five volts.
大概4到5伏
The green curve rising up to around 18 volts is the source voltage.
上升至18伏的绿色曲线是电源电压
And the yellow line is the voltage across the resistor.
黄色的线是电阻两端的电压
So after just a few nanoseconds,
所以仅在几纳秒之后
this voltage rises to around four volts.
这个电压上升至大约4伏
Since the resistor was a kilo-Ohm,
由于这个电阻是一千欧姆
that means four milliamps of current
那就意味着在该信号环绕电路之前
are flowing in the resistor,
有4毫安的电流
before the signal goes all the way around the circuit.
正在流经这个电阻
So we were transferring about 14 milliwatts of power.
所以我们传输了14毫瓦的能量
This is what 14 milliwatts of light actually looks like.
这就是14毫瓦的灯亮起来的样子
So, yeah, it’s not a fully on bulb,
的确 它不是一个完全亮起来的灯泡
but it is visible light and way more than you would get
但它是可见光 并且比泄漏电流
from just leakage current.
能产生的光要亮得多
Now, some of you may argue,
现在 一些人可能会质疑
it’s unfair to use a little LED when I showed a bulb
在原始视频中我使用的是一个灯泡和车载电池
and car battery in the original video,
而现在用一个小LED灯是不公平的
but those items were for illustrative purposes only.
但这些物件只是为了解释说明而已
The clue that this is actually a thought experiment
这实际上是一个思维实验 想法就是
is the two light-seconds of super conducting wire
使用两根30万千米长的
that stretch out into space.
延伸至太空的超导电线
This is not an engineering question about how best
这不是一个类似于怎样在你的卧室
to wire up a light bulb in your bedroom.
用最优方式安装灯泡这样的工程问题
The question was intentionally vague.
我故意没有明说这个问题
And if you want to choose circuit components
如果你想选用几种
such that the bulb never goes on,
让灯泡永远不会亮的电路元件
you are welcome to do that
我表示很欢迎
and I support your conclusion.
并且我支持你的结论
Just to me, the most interesting way
只不过对我而言 解决这个问题
to approach this problem is to ask,
最有趣的方式是去发问:
how could you make the light go on fastest?
怎样才能让这个灯泡最快地亮起来?
I was worried that those long wires would pick up
我本来还担心那些电线会
all the radio waves passing through,
传输所有经过它们的无线电波
and we wouldn’t even be able to see the signal for that noise,
由于噪音的存在 我们甚至都无法分辨出信号
but you can see clearly on the graph
但是你可以在图表上清楚地看见
that the signal is way above the noise level.
这些信号远在噪音水平之上
Alpha Phoenix set up a kilometer of wire
Alpha Phoenix建了一个一千米的电路
and got a very similar result.
并得到了相似的结果
So the light bulb turns on a little bit,
所以 这个灯泡亮了一点
and then after one light-speed delay,
1光速之后
the light bulb turns on the rest of the way.
这个灯泡便一直亮下去了
YouTuber, ZY, simulated the transmission line circuit,
油管人ZY模拟了这个输电线路
and found that even with realistic assumptions,
然后发现即使在现实假设之下
he transferred 12 milliwatts to the load straight away.
他立刻向负载传输了12毫瓦
Derek is actually more correct than we give him credit for.
Derek实际上比我们所认为的更正确
So, I believe that he’s correct on all counts.
所以我完全相信 他是正确的
And the question is neither deceptive
那么 这个问题并不具有迷惑性
or requires like technicalities.
也不需要技术性的细节
So everyone agrees that a steady, small,
所以每个人都同意这个观点:在开关闭合之后
but way-bigger-than-leakage-current signal
一种稳定的 小的
flows through the load in the first second
但是远比泄漏电流大的信号
after the switch is closed.
在第一秒时流经了负载
Is it enough to emit light?
它足够使灯泡发光吗?
Yes, if you use an LED.
当然 如果你用的是一个LED灯泡
But the point of the thought experiment
但是这个思维实验的意义在于
was to reveal something that’s normally hidden
揭露一些在我们看待或者教授电路时
by the way that we think about and teach electric circuits.
隐藏的的知识
You know, we use voltage and current and lumped elements
你懂的 我们使用电压 电流和集总元件
because they’re more convenient
是因为比起用麦克斯韦方程求解
than working with Maxwell’s equations,
它们要更方便
but we shouldn’t forget that the main actors are actually the fields.
但我们不能忘记 主要的因素实际上是场
They are what carry the energy,
它们才携带能量
and you don’t have to take my word for it.
并且这并不是我提出的观点
This is Rick Hartley,
这是Rick Hartley
a veteran printed circuit board designer.
一位资深的印刷电路板设计师
I used to think in terms of voltage and current.
我过去常常从电压和电流方面来思考
And I used to think that the energy in the circuit
并且我过去常常认为电路中的能量
was in the voltage and current, but it’s not.
存在于电压和电流中 但其实不是这样的
The energy in the circuit is in the fields.
电路中的能量存在于场
The most important thing you need to know
你应该了解的最重要的事情是
is that when you route a trace,
当你跟踪一个路由时
you better define the other side of that transmission line,
你最好明确一下输电线路的另外一边
because if you don’t, those fields are gonna spread
因为如果你不这样做 这些场将会蔓延
and they’re gonna leave you an unhappy individual.
你会不快乐
I think one of the things that I’m most excited
我认为这个电路视频让我最激动的事情之一
about the circuit’s video was the response videos I saw
是我看到了许多 由很多人特别是
by so many people especially people
在电气工程方面比我更有资质的人
with far better credentials in electrical engineering than me.
所制作的回应视频
I really enjoyed watching those videos.
我真的很喜欢看那些视频
So I feel like my circuits video was kind of like,
所以我感觉在我的电路视频中
a mistake on my part in certain ways
我的一个错误是
that I didn’t delve deep enough
在一定层面上
into this part of the problem.
我没有足够深入探究这方面的问题
I honestly didn’t think that this was the focus of the video,
诚然 我认为这不是该视频的重点
but clearly everyone who watched it did,
但很明显 每个看过视频的人都觉得是
so that’s on me, but by making that mistake,
所以这怪我 因为我犯了那个错误
and by not going deep into my explanation,
而且没有深入地解释
I invited seemingly a whole bunch of other people
我还邀请了另外一大群人来解释
to make explanations, which I thought were great.
那些问题我原本以为已经解释得很棒了
And some people like Alpha Phoenix even took up
并且其中有人 像Alpha Phoenix 甚至
the challenge and set up his own version of the experiment.
接受了这个挑战并建立了他自己版本的实验
So, frankly, I’m just really excited at what came about,
所以坦白讲 虽然我承认刚开始是我的错
even though I do acknowledge that this was my fault in the first place.
但随之而来的事让我感到太激动了
Like I should have done a better explanation,
我本应该做出更好的解释
but by not doing so, you know,
但是你懂的 因为没有这样做
there are a lot of great explanations out there.
所以涌现出了很多很棒的解释
And that’s what I love.
这就是我乐于见到的
So I’m gonna recommend a whole bunch
所以我想向你推荐一群
of electrical engineering YouTubers to you
电气工程方面的油管人
in case you wanna check those out
万一你要看一看他们的视频
because they’re a lot of great channels,
因为他们的频道很棒
and you should really see how they think about electronics,
你真该见识一下他们是如何思考电子学的
and how they explain this circuit.
以及他们是怎样解释这个电路的
Hey, this video was sponsored by Brilliant,
嗨 这个视频是由Brilliant网站赞助的
the website and app that gets you thinking deeply
该网站和app能够让你对数学 科学
about concepts in math, science, and computer science.
以及计算机科学的概念有深层次的理解
Brilliant is sponsoring a lot of our videos this year,
今年Brilliant赞助了我们很多的视频
because they know someone who makes it to the end
因为他们知道
of a Veritasium video is exactly the sort of person
能把真理元素的视频看到结尾的人
who would love to learn with Brilliant.
正是喜欢用Brilliant学习的那种人
And they have a great course on electricity and magnetism,
并且在电学和磁学方面 他们有一个很棒的课程
which methodically steps you through an introduction
这个课程用问题 模拟 视频和实验
to E&M with questions, simulations, videos, and experiments.
系统地一步一步引导你入门电学和磁学
I really think this is the best way to learn
我真的认为这是最好的学习方式
because the sequence of steps is so well thought out.
因为这些步骤的顺序都是被精心设计的
The difficulty builds gradually.
困难逐渐形成
And by asking you questions,
并且通过询问问题
you are forced to check your understanding at each step.
你不得不检查自己对每一步的理解
If you need help,
如果你需要帮助
there’s always a useful hint or explanation.
课程会有一个有用的提示或者解释
You know what sets Brilliant apart is their interactivity.
让Brilliant与众不同的是它们的交互性
You can learn calculus or machine learning
微积分 机器学习
or computer science fundamentals
或者计算机科学基础
all in this very active way.
你都可以用这种积极的方式来学习
So I encourage you to go over to brilliant.org/veritasium
所以我鼓励你浏览brilliant.org/veritasium网站
and just take a look at their courses.
去看一看它们的课程
I will put that link down in the description.
我会把那个链接放在这段话的下方
And if you click through right now,
并且如果你马上点击进入网址
Brilliant are offering 20% off
Brilliant将会提供20%
an annual premium subscription
年度订阅费津贴
to the first 200 people to sign up.
给前200名注册的人
So I want to thank Brilliant for supporting Veritasium.
感谢Brilliant对真理元素的支持
And I wanna thank you for watching.
感谢大家的观看

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视频概述

你知道电是怎样从发电厂输送到你家的吗?回路中的灯泡需要多久能亮起来?Ve元素带你走进电的世界!

听录译者

收集自网络

翻译译者

Tiffany

审核员

审核员IBRT

视频来源

https://www.youtube.com/watch?v=oI_X2cMHNe0

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