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Does Gauss law holds for any closed surface or it only holds for only Gaussian surface.

Are every closed surface a Gaussian surface?

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Gauss's law holds for any closed surface. the point is thought that when you choose your surface wisely (such as a sphere for a point charge or a cylinder for a line of charge) you can use symmetry and don't have to be able to use heavy-duty vector calculus. So yes, Gauss's law does hold for any surface. But it is a lot easier for some surfaces.

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Any closed surface can be considered as a Gaussian surface, see this wikipedia. The important thing to note is that a Gaussian surface is an arbitrary, closed surface. The reason for this is that as long as it is closed any surface will capture all the flux flowing out from inside it. In practise you may wish to select a more sensible shape, such as a sphere, cylinder or pill-box to make calculation easier.

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  • $\begingroup$ Isn't orientability a necessary condition? $\endgroup$ – jinawee May 21 '14 at 14:15
  • $\begingroup$ @jinawee Yes probably, you have to do the surface integral which requires the surface normal. Can't say I've thought about it that deeply though. $\endgroup$ – nivag May 21 '14 at 14:34

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