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I'm running through the following problem in an EM text of mine:

Calculate the flux of a point charge Q at the origin through a cube centered through the origin by both direct integration and Gauss's Law (essentially prove Gauss's Law for a point charge). Now I got the answer of Q/ε

I have that

Where

Every time I take the divergence of

I basically tried generalizing doing the partial derivative instead of doing a derivative for each coordinate. Let s be the coordinate that I'm differentiating with respect to (i.e. I'm looking at ∂E

Calculate the flux of a point charge Q at the origin through a cube centered through the origin by both direct integration and Gauss's Law (essentially prove Gauss's Law for a point charge). Now I got the answer of Q/ε

_{0}via direct integration alright. When I go to use Gauss's Law in Cartesian coordiantes I keep getting zero, however if I "surround" the cube with an imaginary spherical surface and take the flux through that in Spherical I get the correct answer. I'm trying to reconcile the discrepancy and the only thing I can come up with is that I might have to incorporate the Dirac-Delta Function to account for the fact that I'm dealing with a point charge to do this in Cartesian. Is this accurate to assume?I have that

**E(**=(Q/4πε**r**)_{0})(r^{-3})(**r**)Where

**r**=x**i**+y**j**+z**k**Every time I take the divergence of

**E**in Cartesian and simplify, I end up getting zero.I basically tried generalizing doing the partial derivative instead of doing a derivative for each coordinate. Let s be the coordinate that I'm differentiating with respect to (i.e. I'm looking at ∂E

_{s}/∂s) in figuring out the divergence (i.e. ∂E_{x}/∂x+∂E_{y}/∂y+∂E_{z}/∂z). I am taking the E_{s}to be (Q/4πε_{0})*s*(s^{2}+r^{2}+t^{2})^{-3/2}where r and t are the other coordinates which are not being taken a derivative for. For ∂E_{s}I keep getting (Q/4πε_{0})*(s^{2}+r^{2}+t^{2})^{-5/2}*(r^{2}+t^{2}-2s^{2}). When I apply this to each coordinate choice (s=x,s=y,s=z) and try to take the sum to get the divergence, I keep getting zero.
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