At the risk of sounding imbecilic, I'm going to pose this question anyway.(adsbygoogle = window.adsbygoogle || []).push({});

If I integral a vector function over a surface {a defined region R on a surface S} then what in fact am I doing? I know it sounds bizarre but I can see the logic of the process to find surface areas..but what does this actually represent.. I know its the integral of the vector function and the unit normal vector dotted together, but what is this actually doing? Is this saying how much area this function will trace out in this defined region or what?

I am reading Div, Grad, Curl by H M Schey and I get the idea in the main, but what stumps me is when the author says:

"We evaluate the function F(x,y,z) and this point and form its dot product with [itex]\mathbf{\hat{n}}[/itex]. The resulting quantity is then multiplied by the area [itex]\Delta S[/itex]"

In this case he's talking about dividing up the surface into N faces, then taking the limit of the sum to form the integral etc..etc..

But I dont understand the essence...I can do the algebra and the calculus; thats not an issue..but the underlying essence of it I cannot grasp. If I integrate : [itex]\iint_s \mathbf{F}(x,y,z)\cdot\mathbf{\hat{n}} dS[/itex] then just what the heck is going on, what does the resulting quantity represent?

Sorry if I sound like a fool, but there's probably something obvious I've yet to have spotted.

Thanks guys!!

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# Surface Integrals

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