并且不论在哪里定义，旋度都为零。

And, wherever it's defined, it's curl is zero.

youdao

假设有一个旋度为零的向量场。

OK, so let's assume that we have a vector field whose curl is zero.

youdao

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.

youdao

问题是一个力场的旋度代表什么？

The question is what does the curl of a force field mean?

youdao

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.

youdao

两三周后我们会讲到空间上的旋度？

We are going to see curl in space in two or three weeks. Yes?

youdao

如果旋度是0，那么积分结果就是。

And, if the curl is zero, then I will be integrating zero.

youdao

平面上的旋度公式有些复杂。

And, the formula for curl in the plane was kind of complicated.

youdao

首先你需要计算f的旋度。

You have first to compute the curl of f.

youdao

那个关于电场旋度的方程。

That one tells you about the curl of the electric field.

youdao

当然在物理上，可能遇到的是空间的旋度。

Of course, in physics maybe you have seen curl in space.

youdao

我先讲讲在三维中的旋度。

Let me start by telling you about curl in 3d.

youdao

这个量叫向量场的旋度。

That is called the curl of a vector field.

youdao

实际上，场的旋度是。

In fact, the curl of the field is one, one, one.

youdao

这是旋度F的z分量。

That's the z component of curl F.

youdao

旋度也出现了，那就是格林定理。

That was Greene's theorem.

youdao

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.

youdao

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.

youdao

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.

youdao

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.

youdao

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.

youdao

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?

youdao

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.

youdao

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.

youdao

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.

youdao

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.

youdao

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.

youdao

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.

youdao

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.

youdao

这个场里没有旋度，旋度是不度量拉伸之类的东西的。

There is no curl. This is not what curl measures.

youdao