A charge Q is placed at the centre of a cube. Let phi denote the electric flux due to Q. Which of the following is correct regarding flux through various faces/portions of the cube?

phi_ABCD = Q / (6*epsilon0)
phi_Cbpf = Q / (24*epsilon0)
phi_abed = 0
phi_hbed = Q / (2*epsilon0)

Correct answer: phi_ABCD = Q / (6*epsilon0)

Solution

Gauss's law gives total flux = Q/epsilon0. By the six-fold symmetry of the cube, each square face ABCD receives Q/(6*epsilon0). Triangular half-face Cbpf would get Q/(12*epsilon0), not Q/(24*epsilon0), making option B incorrect; options C and D are also incorrect by symmetry.

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