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Charge q is very close to vertex a, so I'm treating it as if it were on vertex a, and I'm trying to get the flux going through the 3 surfaces intersected at g, and the answer my book gives me is 1/8 q/ε0

I don't understand where the 1/8 comes from, I tried drawing a gaussian surface passing by point a and centered at g but I'm going to have to do the integral instead of direct use of q/ε0 , can you help?

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  • $\begingroup$ Hint: Consider the charge at the center of a larger box made up of 8 of those boxes in the figure. You don't need to do any integrals. Also, the problem should say the faces the meet at g, right? $\endgroup$ – BioPhysicist Aug 2 '18 at 2:22
  • $\begingroup$ No, the problem is correct, the flux inside the box is zero, so I'm taking the flux through faces meeting at g to find out the flux through faces meeting at a $\endgroup$ – khaled014z Aug 2 '18 at 9:54
  • $\begingroup$ And I still really don't understand why do I have to do it as 8 boxes, why the number 8? $\endgroup$ – khaled014z Aug 2 '18 at 9:56
  • $\begingroup$ Imagine the charge at the origin of a Cartesian coordinate system. Now in each octant, put one of those cubes such that a corner is also touching the origin. Treating this as one large cube, your charge is inside of it, so you know the total flux through all of the outside surfaces is $\frac {q}{\epsilon _0}$. Now, how can you use the symmetry of the system to say how much flux goes through the three outer surfaces of just one of the smaller cubes? $\endgroup$ – BioPhysicist Aug 2 '18 at 10:52
  • $\begingroup$ You don't have to do it as 8 boxes. I am sure there are many ways to think of this problem. This is the easiest to me though, and doesn't require performing any integrals. $\endgroup$ – BioPhysicist Aug 2 '18 at 10:56

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