Magnetism and Electromagnetism
AP Physics 2 Topic 12 9:21 English narration · English + 中文 subtitles burned in
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High over the Arctic, the night sky glows green.
在北极上空，夜空泛起绿光。
These curtains of light are not fire. They are charged particles from the Sun, arriving at a million kilometres an hour.
这些光帘不是火焰，而是太阳抛出的带电粒子， 以每小时上百万公里的速度扑向地球。
Something invisible catches them, bends their paths, and steers them to the poles, where they hit the air and make it glow.
有一种看不见的东西抓住它们，让它们的路径弯曲， 把它们引向两极；在那里它们撞上空气，使空气发光。
That something is Earth's own magnetic field.
这个东西，就是地球自己的磁场。
A magnetic field bends every moving charge.
磁场会让每一个运动的电荷转弯。
This is Unit Twelve: magnetism and electromagnetism.
这是第十二单元：磁与电磁学。
Magnets and electricity look like two separate subjects. They are not.
磁和电看起来像两个不同的课题，其实不是。
Moving charge makes a magnetic field, and a changing magnetic field makes charge move.
运动的电荷会产生磁场，而变化的磁场会让电荷运动起来。
Let's begin.
让我们开始吧。
A magnetic field is a vector field: at every point it has a size and a direction, and we draw it with field lines.
磁场是一个矢量场：它在每一点都有大小和方向，我们用磁感线把它画出来。
Outside a bar magnet they leave the north end and return to the south end.
在条形磁体外部，磁感线从北极出发，回到南极。
Field lines always close into loops; they never begin or end in empty space.
磁感线总是闭合成环， 绝不会在空处开始或结束。
Put a small compass anywhere in the field and it turns until it points along the line it sits on.
把一个小指南针放进磁场里，它会转动， 直到指向它所在的那条磁感线的方向。
Where the lines crowd together, the field is stronger.
磁感线越密的地方，磁场越强。
And magnetic poles always come in pairs — you never get a single one: cut a magnet in half and you get two — like poles push apart, opposite poles pull together.
而且你永远得不到单独的一个磁极：把磁体切成两半，只会得到两块磁体—— 同名磁极互相排斥，异名磁极互相吸引。
Magnetic dipoles come from charge moving in circles — in matter, that means the electrons.
磁偶极子来自做圆周运动的电荷——在物质内部，就是电子的运动。
Iron, nickel and cobalt are ferromagnetic: their dipoles line up strongly and stay lined up, which makes permanent magnets.
铁、镍、钴是铁磁性材料：偶极子排列得很强，而且会保持排列，所以能做成永磁体。
Aluminium and titanium are paramagnetic: they line up weakly and lose it once the field is gone.
铝和钛是顺磁性材料：排列很弱，外磁场一撤就消失。
Diamagnetic materials — in fact every material has some diamagnetism — align weakly the other way.
所有材料还都具有抗磁性，也就是朝相反方向的微弱排列。
Permeability measures that response: fixed for free space, different in matter, and not even constant there.
磁导率衡量这种响应：真空有一个固定值；物质与它不同，而且不是常数。
Now put a charge into a magnetic field.
现在把一个电荷放进磁场里。
A charge sitting still feels nothing.
静止的电荷什么也感受不到。
Send it across the field and it feels a push — and look where that push points.
让它横穿磁场，它就受到一个推力——注意这个推力指向哪里。
It is always at right angles to the motion, so it can never speed the charge up or slow it down.
它始终与运动方向垂直，所以既不能让电荷加速，也不能让它减速，只能让它转向。
It only turns it. Constant turning at constant speed is a circle.
以不变的速率不断转向，走出来的就是一个圆。
The size of the force is the charge, times the speed, times the field, times the sine of the angle between the velocity and the field.
这个力的大小等于电荷量，乘以速度，乘以磁场，再乘以速度与磁场夹角的正弦。
So the angle matters: it is largest when the charge cuts straight across the field, and zero when it travels along it.
所以夹角很重要：电荷垂直横穿磁场时力最大，沿着磁场方向运动时力为零。
For the direction, use your right hand: fingers along the velocity, curl them into the field, thumb gives the force on a positive charge — reverse it for a negative one.
方向用右手判断：四指指向速度方向，弯向磁场方向，大拇指就给出正电荷所受的力； 负电荷则方向相反。
And because that force is always sideways to the motion, it does no work, so the speed never changes.
又因为这个力始终与运动方向垂直，所以它不做功，速率也不变。
A proton enters a field of half a tesla at two hundred thousand metres per second, at right angles to it.
一个质子以每秒二十万米的速度垂直进入零点五特斯拉的磁场。
The force is the charge, times the speed, times the field: about one point six times ten to the minus fourteen newtons.
力等于电荷量乘以速度再乘以磁场，约为一点六乘以十的负十四次方牛顿。
That force is centripetal, so the proton bends into a circle.
这个力就是向心力，所以质子被弯成一个圆。
Set it equal to mass times speed squared over the radius, cancel one speed, and the radius is the momentum divided by the charge times the field.
令它等于质量乘以速度平方再除以半径， 约掉一个速度，半径就等于动量除以电荷量与磁场的乘积。
That gives four point two millimetres — how a mass spectrometer sorts ions: heavier ones curve wider.
算出来是四点二毫米——质谱仪分离离子，用的正是这个道理：更重的离子弯得更开。
Two quick extras.
还有两个小要点。
First, if a region holds both an electric field and a magnetic field, a moving charge feels both forces, and they act independently: work out each and add them as vectors.
第一，如果一个区域里既有电场又有磁场，运动的电荷会同时受到两个力， 而且互不影响：分别算出来，再按矢量相加。
Second, send a current along a metal strip and put a field across it.
第二，让电流沿着一条金属薄片流动，再加上一个横向的磁场。
The magnetic force pushes the moving charges to one side, and a voltage appears across the strip.
磁力把运动的电荷推到一侧，薄片两侧就出现电压。
That is the Hall effect, and it is how many magnetic sensors work.
这就是霍尔效应， 也是许多磁传感器的工作方式。
Even a single moving charge makes a magnetic field of its own — the faster it moves, the stronger the field.
即使是单个运动的电荷，也会产生自己的磁场——它运动得越快，磁场越强。
A current is a stream of moving charge, so a current makes a field too.
电流就是一连串运动的电荷，所以电流也会产生磁场。
Around a long straight wire the field lines are circles wrapped around it: never pointing outward, never along it.
在一根长直导线周围，磁感线是绕着它的一圈圈同心圆：既不指向外，也不沿着导线。
For the direction, grip the wire with your right hand, thumb along the current, and your fingers curl the way the field goes.
想知道绕的方向，就用右手握住导线，大拇指指向电流方向，四指弯曲的方向就是磁场的方向。
How strong is it?
它有多强呢？
The field is the permeability of free space, over two pi, times the current divided by the distance from the wire.
磁场等于真空磁导率除以二派，再乘以电流除以到导线的距离。
Double the current and the field doubles; go twice as far away and it halves.
电流加倍，磁场就加倍；距离变成两倍，磁场就减半。
Bend the wire into a loop, and the field at the centre runs along the loop's axis — right hand again.
把导线弯成一个圆环，环心处的磁场沿着环的轴线——还是用右手判断。
Stack many loops into a solenoid and it acts like a bar magnet.
把许多圆环叠成螺线管，它就像一块条形磁体。
So a current creates its own magnetic field, which is how electromagnets and motors work. Near two wires, add the two fields as vectors.
在两根导线附近，把两个磁场按矢量相加。
A field pushes on moving charge, so it pushes on a current-carrying wire.
磁场会推运动的电荷，所以它一定也会推载流导线。
The force is the current, times the length, times the field, times the sine of the angle between them — and only the length inside the field counts.
这个力等于电流，乘以长度，乘以磁场，再乘以两者夹角的正弦—— 而且只有处在磁场里的那一段长度才算数。
Right-hand rule again for the direction, and this push turns every electric motor.
方向依然用右手定则判断。 正是这个推力让每一台电动机转起来。
Now a number: a thirty-centimetre wire carries four amps at right angles to a field of zero point two tesla. Pause and try it.
试一题：一根三十厘米的导线，通过四安培的电流， 垂直横穿零点二特斯拉的磁场。
The answer is zero point two four newtons.
先暂停，自己算一算。 答案是零点二四牛顿。
Induction starts with flux.
感应现象要从磁通量说起。
Magnetic flux measures how much field passes through a surface: the field, times the area, times the cosine of an angle.
磁通量衡量有多少磁场穿过一个面： 磁场乘以面积，再乘以一个夹角的余弦。
The area vector does the work — it points straight out of the surface, and the angle is measured from it, not from the surface.
真正起作用的是面积矢量—— 它垂直指向面的外侧，而夹角是相对这个矢量来量的，不是相对这个面。
Face the loop square-on to the field and the flux is largest; turn it edge-on and the flux is zero.
让线圈正对磁场，磁通量最大；把它转到侧对，磁通量为零。
The sign says whether the field runs with the area vector or against it.
正负号则告诉你磁场是顺着面积矢量，还是逆着它。
Now watch what a change of flux does — electromagnetic induction.
现在看磁通量的变化会带来什么。
Push a magnet into a coil and the meter jumps: a current flows, with no battery anywhere.
把磁体推入线圈，电表指针立刻跳动： 电路里没有任何电池，却有电流流过。
Hold it still inside the coil and the current dies, even though the field through the coil is strong.
把磁体停在线圈里不动，电流就消失了， 尽管穿过线圈的磁场依然很强。
Pull it out and the meter swings the other way.
把磁体抽出来，指针又向另一边偏转。
It is never the flux itself that matters. It is the change.
起作用的从来不是磁通量本身，而是它的变化。
Faraday's law says the induced voltage equals the rate at which the flux changes: quickly for a big voltage, slowly for a small one.
法拉第定律说：感应电压等于磁通量变化的快慢。
Then multiply by the number of turns in the coil.
变得快，电压就大；变得慢，电压就小；再乘以线圈的匝数。
There are exactly three ways to change the flux: change the field, change the area, or turn the loop.
改变磁通量恰好只有三种办法：改变磁场、改变面积，或者转动线圈。
The minus sign is Lenz's law: the induced current flows so that its own field opposes the change that made it.
那个负号就是楞次定律：感应电流的方向，总是让它自己的磁场去阻碍产生它的那个变化。
If you push a north pole in, the induced current makes a north pole facing the magnet, so they push apart.
如果你把北极推进去，感应电流会在面对磁体的一侧做出北极，于是两者相斥。
If it helped instead, energy would come from nowhere.
如果反过来去帮忙，能量就会凭空产生。
The flux through one loop falls from zero point zero two zero webers to zero point zero zero eight webers in thirty milliseconds. Find the average induced voltage. Pause the video and try it.
穿过一个线圈的磁通量在三十毫秒内从零点零二零韦伯降到零点零零八韦伯， 求平均感应电压。
The flux changed by zero point zero one two webers; divide by thirty milliseconds and you get zero point four zero volts.
先暂停，自己算一算。 磁通量改变了零点零一二韦伯， 除以三十毫秒，得到零点四零伏。
Wind it into a coil of two hundred turns and the voltage becomes eighty volts — which is why generators use many turns.
把同一个线圈绕成二百匝，电压就变成八十伏——这正是发电机要用很多匝线圈的原因。
One arrangement appears again and again in exams: a metal rod sliding along two rails in a magnetic field.
有一种装置在考试里反复出现：一根金属杆在磁场中沿着两条导轨滑动。
The field never changes and nothing turns — only the area changes.
这里磁场不变，也没有转动——只有面积在变。
As the rod slides, the circuit's area grows at the rod's length times its speed.
杆滑动时，电路面积增长的快慢等于杆长乘以速度。
Multiply by the field, and that is how fast the flux grows, so the induced voltage is the field, times the length, times the speed.
再乘以磁场，就是磁通量增长的快慢，所以感应电压等于磁场，乘以杆长，再乘以速度。
Push the rod faster, and the voltage rises in proportion.
杆推得越快，电压就成比例地升高。
Now put it all together.
现在把这些串起来。
Spin a coil between the poles of a magnet.
让一个线圈在磁体两极之间旋转。
Nothing moves in or out; the loop simply turns, so the angle changes, the flux changes, and a voltage appears.
没有任何东西进出，线圈只是在转，于是夹角在变，磁通量在变，电压就出现了。
Every half turn the voltage reverses — that is alternating current.
每转半圈，电压就反向一次——这就是交流电。
Coal, water, wind, sunlight: they all end at a coil turning near a magnet.
煤、水、风、阳光：它们最后都归结为一个线圈在磁体旁边转动。
Three marks students lose here.
这里有三个学生常失的分。
First, the magnetic force is perpendicular to the velocity, so it changes direction but never speed — and a charge at rest, or moving along the field, feels nothing.
第一，磁力与速度垂直， 所以它只改变方向，绝不改变速率——静止的电荷，或沿磁场方向运动的电荷， 完全不受力。
Second, induction needs a changing flux; a magnet held still inside a coil induces nothing, however strong it is.
第二，感应需要变化的磁通量：磁体静止地停在线圈里， 再强也不会产生感应。
Third, keep the minus sign honest, and don't forget the number of turns.
第三，别忽略那个负号，也别忘了乘以匝数。
Get those right, and this unit is yours.
把这些做对，这个单元就是你的了。