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"The four faces of a tetrahedral pyramid are equilateral triangles of a side

**Such a pyramid sits with one face flat on an infinite sheet of charge with a surface charge density**

*a**. What is the flux through the face of the pyramid that sits on the sheet? What is the flux through each of the other three faces?"*

**sigma**My solutions manual tells me that I should treat the surface charge as positive. From that I can calculate the electric field algebraically as

**. Apparently because of that the electric flux is:**

*E = -(sigma)/(epsilon nought)*

*[(3)*^{1/2}/(8)] x [(sigma)/(epsilon nought)] x [a^{2}]From what it describes, the pyramid itself contains no net charge, so the total flux through all of its faces must be zero. The area vectors for the remaining three faces all point outward and give a positive total flux. Since the total flux is zero, the flux of each of the remaining faces is:

**.**

*[(3)*^{1/2}/(24)] x [(sigma)/(epsilon nought)] x [a^{2}]Can someone please explain how they went about calculating these equations algebraically .