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A point charge q is placed at one corner of a cube. What is the electric flux of the field E through one of the three faces of the cube that do NOT touch that corner (a face lying opposite to the charge)?

1. q/(4*epsilon0)
2. q/(24*epsilon0)
3. q/(48*epsilon0)
4. q/(8*epsilon0)

Correct answer: q/(24*epsilon0)

Solution

By Gauss's law the total flux from q is q/epsilon0. Surrounding the corner charge by 8 such cubes, each cube intercepts (1/8)(q/epsilon0) = q/(8*epsilon0). Within one cube, the three faces meeting at the corner have the field lines grazing along them, contributing no net flux. The other three faces share the cube's flux equally, so each gets one third of q/(8*epsilon0), giving q/(24*epsilon0).

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