A friend of mine asked me what is the flux of the electric field (or any vector field like
$$
\vec r=(x,y,z)\mapsto \frac{\vec r}{|r|^3}
$$ where $|r|=(x^2+y^2+z^2)^{1/2}$) through a Mobius strip. It seems to me there are no way to compute it in the "standard" way because the strip is not orientable, but if I think about the fact that such a strip *can* indeed be built (for example using a thin metal layer), I also think that an answer *must* be mathematically expressible.

Searching on wikipedia I found that

http://en.wikipedia.org/wiki/Mobius_resistor

A Möbius resistor is an electrical component made up of two conductive surfaces separated by a dielectric material, twisted 180° and connected to form a Möbius strip. *It provides a resistor which has no residual self-inductance, meaning that it can resist the flow of electricity without causing magnetic interference at the same time.*

How can I relate the highlighted phrase to some known differential geometry (physics, analysis?) theorem?

Thanks a lot!