I was supposed to compute the curl of a field for a fairly simple assignment and got the following :
$$\nabla \times F = (0,0,y-e^{x+y}) \text{ ; } (x,y) \in [0,1]\times [0,1]$$
However, I'm unable to appreciate the meaning of this and I hate doing things like a machine. I tried a few different online sources, but I still don't know how to interpret my result.
Can someone explain, in a natural manner, what implications does my result have ?
Best Answer
Sorry I cant comment, because my reputation is not big enough, so I will just answer...
Imagine you throw a ball inside the vector field. This ball starts to move alonge the vectors and the curl of a vectorfield is a measure of how much the ball is rotating. The curl gives you the axis around which the ball rotates, its direction gives you the direction of the orientation (clockwise/counterclockwise) and its length the speed of the rotation.
This is some curde model to give you some imagination about the curl...