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Please bear with me for another few days...I promise I'll get this done as fast and as painlessly as possible.

Here goes...

1.In divergence theorem,green's theorem and stoke's theorem,we

**basically interchange between types of integrals-e.g green's theorem lets us interconvert line integrals and surface integrals**.....do we need to interchange between types of integrals just to aid calculations?

2.Why does curl need to be a vector quantity? The concept curl(i.e

**the amount of rotation at a particular point**) could be explained by a scalar quantity also...we wouldn't need to assign a direction?

3. Why is an irrotational field nonconservative?

(I found a website describing an irrotational field as one in which there is 'free energy'....what's this all about?)