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In the past few weeks, I have been trying to gain a basic understanding of classical electricity and magnetism through the fantastic lectures at http://ocw.mit.edu, specifically the physics course 8.02 taught by Dr. Walter Lewin.

In his explanation of electric flux (lecture 3), he derives Φ for an arbitrary sphere of radius R containing charge Q, and comes up with Φ = Q/ε_{0}, as expected per Gauss's Law. He then explains thatanyclosed surface containing charge Q will have that same flux.

Exploiting symmetry with a sphere, the calculation is fairly easy, so I wanted to challenge myself and see if I could calculate the flux for a uniform cube with a charge Q at its center. I am finding the problem unexpectedly difficult and I'm not even sure what kind of integral to construct.

Is this too ambitious to calculate given my little experience in this area? My calculus skills are rusty, but I am eager to learn and enjoy a challenge.

My only reasoning so far is that the total flux through the cube would be 6 times the flux through a single plane, so I am approaching the problem by trying to calculate the flux through a square on the xy-plane with 1 corner at the origin and charge Q under it. While the normal at every point is the same, simply constructing the correct expression for the changing E-field vector and the correct integral is kicking my butt :P

Any tips or suggestions to point me in the right direction are appreciated!

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# Calculating Electric Flux Φ w/o typical Gaussian surface

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