电场的旋度，在二者间产生了电压。
And the curl of the electric field will generate voltage between these two guys.
旋度会计算出，发生了多大的旋转。
And the curl will compute how much rotation is taking place.
首先你需要计算f的旋度。
那个关于电场旋度的方程。
我先讲讲在三维中的旋度。
这个量叫向量场的旋度。
这是旋度F的z分量。
旋度也出现了，那就是格林定理。
当你计算这个式子时，不要把它当做旋度来算。
The calculation of this thing, once you've computed curl does not remember that it was a curl.
旋度衡量的是,在某点上的旋转的程度。
And what a curl will measure is how intense the rotation effectis at that particular point.
如果旋度是0，就意味着，这个力不产生旋转作用。
And if the curl is zero then it means that this force does not generate any rotation effects.
这不矛盾，但是，想象一下，在这里旋度是没有定义的。
There's no contradiction. And somehow, you have to imagine that, well, the curl here is really not defined.
力场的旋度告诉你，角速度增加或减小的快慢。
And the curl of a force field tells you how quickly the angular velocity is going to increase or decrease. OK.
我们知道旋度是度量旋转的，那散度表示什么？
I mean, we said for curl, curl measures how much things are rotating somehow. What does divergence mean?
如果旋度为0，而且场处处有定义，那么它就是保守场。
If the curl is zero, and if the field is defined everywhere, then it's going to be conservative.
如果旋度在原点有定义，你就可以试试了，计算二重积分。
So, if a curl was well defined at the origin, you would try to, then, take the double integral.
在这个新说法中，在那有个条件，条件表明f的旋度等于。
In this new language, the conditions that we had over there, 0 this condition says curl F equals zero.
不过很快就会变得十分便利的，因为我们很快就会学到旋度。
It's going to become very handy pretty soon because we are going to see curl.
最后一个说明了，磁场的旋度，是如何由电荷的运动产生的。
And the last one tells you how the curl of the magnetic field is caused by motion of charged particles.
真是十分幸运啊，因为如果旋度是0，那么场至少是保守的。
And that would be fortunate because if a curl is zero then your field is less conservative.
如果场是保守的-，如果旋度是0，那么右手边的结果也会是。
See, if your field was conservative — 0 if a curl was zero then the right-hand side would just be zero.
这个场里没有旋度，旋度是不度量拉伸之类的东西的。
实际上，Maxwell方程组，描述了这两个场的旋度和散度。
Maxwell's equations actually tell you about div and curl of these fields.
特别地，一个没有旋度的力场，就是一个不产生任何旋转运动的力场。
In particular, a force field with no curl is a force field that does not generate any rotation motion.
旋度实际上衡量的是，在任意给定点,运动旋转角速度的两倍。
The curl actually measures twice the angular speed of a rotation part of a motion at any given point.
当需要判断一个向量场是否保守向量场时,旋度也会派上用场的。
One place where it comes up is when we try to understand whether a vector field is conservative.
空间中的向量场的旋度，是一个向量场，而不是一个标量函数，我必须告诉你们。
The curl of a vector field in space is actually a vector field, not a scalar function. I have delayed the inevitable.
关于旋度的更多介绍，设有一速度场，我们知道旋度是测量旋转影响的。
More about curl.If we have a velocity field, then we have seen that the curl measures the rotation affects.
旋度是下周的内容，你们习惯这个记号就行了，你们可能已经在物理课上用到过了。
Curl will be for next week. Just getting you used to the notation, especially since you might be using it in physics already.
这就是问题所在，如果你想积分，我们需要它处处有定义，旋度是0，那么你的积分也是。
OK, so that's the problem. I mean, if you try to integrate, we've said everywhere where it's defined, 0 the curl is zero. So, what you would be integrating would be zero.
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