So this vector field is not conservative .

所以，这个 向量 场不是保守场。

I want to find the potential for this vector field .

我想找出这个 向量 场的势函数。

But it 's a new vector field that you can build out of f.

这是一个新的 向量 场，可以用f来建立。

It is a vector field in some of the flux things and so on .

也可以是一个 向量 场的通量，等等。

The electric current density vector field also satisfies superposition principle some applications thereof are introduced .

电流密度 矢量 场也满足叠加原理，给出了一些应用电流密度场叠加原理的例子。

It is proportional to this vector field .

它与 向量 场成比例。

So it 's an example of a vector field that is not conservative .

这是一个非保守 场的例子。

If you take the gradient of this you should get again this vector field over there .

对这个函数取梯度，你应该又得到这个 向量 场。

Let 's say that I have a plane curve and a vector field in the plane .

有一条平面曲线和这个平面上的 向量 场。

Just to remind you a vector field in space is just the same thing as in the plane .

提醒大家，空间中的 向量 场与平面中的相同。

We had a curve in the plane and we had a vector field .

平面上有一曲线，且存在着 向量 场。

So in fact it 's a vector field .

事实上，是一个 向量 场。

And this guy is a function that somehow relates to the vector field .

这是一个在某种方式下，与 向量 场有关的函数。

In fact our vector field and our normal vector are parallel to each other .

事实上，给定的 向量 场与法向量是相互平行的。

Once you have such a formula you do the dot product with this vector field which is not the same as that one .

一旦你得到一个这样的计算式，你对 向量 场做点积，这和前面这个不一样。

It measures how much a vector field goes across the curve .

它度量有多少 向量 场穿过了曲线。

The problem is not every vector field is a gradient .

问题是，不是所有 向量 场都是梯度。

But you can also use it to define a vector field in space just with no z component .

你可以用它来定义，一个没有z分量的空间 向量 场。

We need actually a vector field that is well-defined everywhere .

实际上我们需要，一个处处有定义的 向量 场。

It 's a vector field that just rotates around the origin counterclockwise .

这是一个绕原点逆时针旋转的 向量 场。

And we said this measures how far that vector field is from being conservative .

它度量了， 向量 场与保守场的距离。

That is my curve and my vector field .

那就是曲线和 向量 场。

I have a curve in the plane and I have a vector field .

这有一条平面曲线和一个 向量 场。

Let 's say I want to do it for this vector field .

比如说，我想对这个 向量 场来 求解。

Remember the divergence of a vector field What do these two theorems say ?

向量 场，的散度，这两个定理说了什么呢？

And of course it is not a coincidence because this vector field is a gradient field .

当然这并非巧合，因为这个 向量 场是有势场。

S Let 's say that we have a vector field and s a surface in space .

假设空间中存在一个 向量 场和一个曲面。

It sums up the definition general expressing formula and general calculating method of flux in any vector field by analyzing the flux in the speed field electric field and magnetic field of fluid .

文章通过对流体的速度场、电场和磁场中通量的解析，总结出了任意的 矢量 场通量的定义、一般表达式及一般计算方法。

We are just integrating a vector field that has nothing to do with that .

其实是要对一个与其无关的 向量 场积分，其实是要对一个与其无关的 向量 场积分。

That is called the curl of a vector field .

这个量叫 向量 场的旋度。