This puzzle has two parts, the first part is easier, and once you\'ve got it, it

Question

This puzzle has two parts, the first part is easier, and once you've got it, it becomes a clue for the second part.

The figure above and on the left shows a point charge Q trapped inside a surface that looks rather like a "flying saucer." The charge is at the center of the saucer. Part one of the puzzle is: What is the electric flux through the upper half of the saucer? Give an explanation of the reasoning behind your answer.

The figure above on the right shows the same charge Q embedded in center of the floor of a tetrahedron. Part two of the puzzle is: What is the electric flux through one of the three triangular "walls" of the tetrahedron (not through the floor)? Give an explanation of the reasoning behind your answer.

Explanation / Answer

From electrostatics we know that the flux of electric field through an object is given as

phi = q/epsilon_0
where q is the charge enclosed by a surface of any arbitrary shape.

Therefore,

in the first problem, the flux through the whole of the surface = Q/_0

so the flux through the upper half of the surface should be half of the above value = Q/(2*_0)

Since the electric flux is uniformly distrubuted throughout the surface.

same explanation holds for the tetrahedron case where the charge is situate on the bottom face.

The flux through each of the face should be uniform and so net flux through one of the three triangular walls should be 1/4th of the total flux = Q/(4*_0).

I hope this answers your question! If you have any further query then do let me know! :)

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