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A point charge +Q sits at the centre of the square base of a square pyramid (a pyramid with a square base and four identical triangular slanting faces). Find the electric flux passing through one of the four identical upper (slanting) faces.

1. Q / 16*epsilon0
2. Q / 4*epsilon0
3. Q / 8*epsilon0
4. None of these

Correct answer: Q / 8*epsilon0

Solution

Place +Q at the centre of a cube; by symmetry the flux through each of the 6 faces is Q/(6*epsilon0). A square pyramid with the charge at its base centre is equivalent to half of such a configuration. The charge sits in the plane of the base, so half the total flux Q/epsilon0, i.e. Q/(2*epsilon0), passes upward through the four slanting faces combined. Each of the four identical faces therefore carries one quarter of that: (Q/(2*epsilon0))/4 = Q/(8*epsilon0).

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