并证明该电场是有源有旋场。
文章还指出在有旋场中也可以定义偶极子的平动势能。
It is pointed out that the translation potential energy of the dipole can be defined even if in the curl field.
这个场里没有旋度，旋度是不度量拉伸之类的东西的。
另一个向量场，是通过计算第一个向量场的旋度得到的，计算旋度之后，就可以得到一个不同的向量场。
That other field is given from the first one just by taking its curl So, after you take the curl, you obtain a different vector field.
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.
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.
我们已经知道了一个准则，如果向量场的旋度为零，而且它在整个平面上有定义，那么这个向量场是保守的，而且它是个梯度场。
Well, we've seen this criterion that if a curl of the vector field is zero and it's defined in the entire plane, then the vector field is conservative, and it's a gradient field.
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.
和平面上的旋度的一个重要的不同点是，这里向量场的旋度，仍然是一个向量场。
Now, an important difference between curl here and curl in the plane is that now the curl of a vector field is again a vector field.
如果取一个有旋的向量场，流体流动方向是环绕某个坐标轴的，那么就会发现它的散度是零。
And, if you take a vector field where maybe everything is rotating, a flow that's just rotating about some axis, then you'll find that its divergence is zero.
这就是F的旋度，在实际应用中，如果你必须计算一个向量场的旋度，不要尝试记忆这个公式。
And that is indeed going to be the curl of F. in practice, if you have to compute the curl of a vector field, you know, don't try to remember this formula.
这个量叫向量场的旋度。
一个向量场,如果定义在单连通区域并且旋度为零，那么它就是一个梯度场，并且其上的线积分与路径无关。
OK, so, we've seen that if we have a vector field defined in a simply connected region, and its curl is zero, then it's a gradient field, and the line integral is path independent.
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.
实际上，场的旋度是。
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.
如果你们做了习题集,发现了和我一样的答案，你就会发现向量场的旋度在曲线上处处为。
So if you've done the problem sets and found the same answers that I did, 0 then you will have found that this vector field had curve zero everywhere.
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.
我们还知道,如果力是由势产生的,那么其旋度是,这就是我们得到的,关于从势产生的向量场的准则。
There is another thing that we know because if a force derives from a potential 0 then that means its curl is zero Thats the criterion we have seen for a vector field to derive from a potential.
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.
通过大量实验，研究了该系统的性能。在多种回流和旋流流场测量中进行了应用。
The characteristics of this system is studied by experimental investigation, and find its use in various recirculating flows and swirling flows.
用五孔探针测试旋流式气力分级机流场时，分级机内存在的静压梯度会对测试产生影响。
The static pressure gradient in cyclone air classifier can have influence on the test and measurement for its flow fields by five-hole probe.
成形过程中的温度场变化对钛合金锥形件温热剪旋成功与否，以及产品的精度影响很大。
Changing of temperature distribution during warm shear spinning of cone workpiece of titanium alloy greatly affects the process and the product's precision.
本文试验研究气力输送管路的旋流流场特征。
Swirl flow field of a pneumatic conveying system is investigated experimentally.
采用针尖的旋抛物面模型，给出了表面生成的负离子在针尖场中飞行的动力学方程，并用数值方法求解。
Adopting paraboloid model of tip surface, presented the dynamics equation of negative ion flight in tip field and solve it with numerical method.
采用激光多普勒测速仪，对超细旋液粉碎器工作腔内流场进行测量和研究。
The flow fields of ultra micro rotary fluid fragment or were measured and investigated by using laser Doppler anemometer.
以加热空气模拟燃气，根据热平衡原理，考察旋流对燃烧器出口处燃气浓度场的影响。
By simulating gas with heated air, the influence of swirling flow on gas concentration field at gas burner is investigated according to the principle of heat balance.
两能级原子与外部环境(热库)相互作用时，采用非旋波近似，研究原子与热辐射场单光子和双光子作用过程。
The interaction of a two-level atom with a thermal radiation field for single-photon processes and two-photon processes without rotating wave approximation is analysed.
试验研究了主、径向涡流器旋流数、面积比、套筒扩张角等参数对双旋流进气装置冷态流场的影响。
The effects of swirl number of primary swirler and radial swirler, area ratio and sleeve divergence angle on the cold flow field of double swirl air intake were investigated.
对于旋流燃烧室内温度场的模拟预报也表明，DO模型的计算结果和实验值相吻合，明显高于用SHF模型计算所得的温度值。
For swirl combustor, the predicted temperature distribution of DO model were in good agreement with those measured by experiment and were better than those of the SHF model.
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