On The Field Hand

Just as wealth and success on the field go hand in hand in today's pro soccer, so can disaster on the field bring disaster at the bank.

就像当今足坛财富与战绩携手同行，球场上的失败同样会导致财政上的崩溃。

Flux, on the other hand, measures, when I go along the curve, roughly how much the field is going to across the curve.

从另一方面来看，“通量”度量的是，沿着曲线前进时，大致会有多少向量场通过曲线。

So, in both cases, we need the vector field to be defined not only, I mean, the left hand side makes sense if a vector field is just defined on the curve because it's just a line integral on c.

了解这两种表述后，我们不仅需要向量场，就是左边这里，这是曲线c上的线积分，向量场在曲线上有定义。