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Suppose I am calculating the (homogenous) electric flux through a straight line. How do I calculate the surface integral of a straight line? Is it simply a line integral, or is it more complex (I don't think the first is true because if the surface integral is a measure of area, but the line integral is a measure of length). I found this on wikipedia.

In mathematics, a surface integral is a definite integral taken over a surface. It can be thought of as the double integral analog of the line integral. Given a surface, one may integrate over its scalar fields (that is, functions which return scalars as values), and vector fields (that is, functions which return vectors as values).

Basically, how do I calculate the surface integral of a line y= mx+c? What about more complex curves, for example the Archimedean Spiral ($r= a+ b \theta$ in polar form)?

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It would help to have more context. Barring the appearance of infinite quantities, the surface integral of a field goes to 0 as the surface is retracted to a line. Analogously, the regular integral over an interval of the real line will go to zero as the interval collapses to a point, unless you have some fishy delta-function stuff going on. –  Chris White Jul 30 '13 at 4:51
    
I guess the big question is, why are you calling it a "surface integral" when what you're integrating over is a curve or a line? There's no surface involved, so I think you're using the word to mean something else. –  Muphrid Jul 30 '13 at 5:16
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1 Answer 1

Suppose I am calculating the (homogenous) electric flux through a straight line. How do I calculate the surface integral of a straight line?

Actually, it's impossible to do this. It's inherent in the definition of flux (in three dimensions, anyway) that you need a surface to serve as the region of integration. You can't do it with a line.

Why did you think you needed to calculate flux along a line, anyway? If you expand on that, I can provide more information.

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