# Why doesn't a gaussian surface pass through discrete charges?

I have read that Gaussian surface cannot pass through discrete charges. Why is it so? I have even seen in application of Gauss' Law when we imagine a Gaussian Surface passing through a charge distribution, e.g. in case of infinite plane charge carrying sheet .

If it cannot pass through discrete charges how do we use it in continuous charge distributions as same 'objection' must be there for it also.

Here $E \rightarrow \infty$ as, $r\rightarrow 0$

If this is ambiguity then this must be same in continuous charge distribution , otherwise please state it more clearly because we can define charge to be a spherical ball and half charge can be considered inside surface (as in pic and even agreed by @JoshuaBarr).

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There is a good discussion of this in the first chapter of Purcell and Morin, Electricity and Magnetism. –  Ben Crowell Mar 22 '13 at 15:21
@BenCrowell If a pdf version of this exist please provide me that , i don't have book –  ABC Mar 22 '13 at 15:51
There's this thing called a library. –  Ben Crowell Mar 22 '13 at 22:42