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A charge q is enclosed by a closed surface made of an inverted cone of height h and base radius R together with a hemisphere of radius R, with the charge at the centre of the flat circular interface. The electric flux through the conical (lateral) surface is n*q/(6*epsilon0). Find the integer/value n. (Construct plausible options.)

1. 1
2. 2
3. 3
4. 4

Correct answer: 2

Solution

With the charge at the centre of the circular boundary, the hemisphere subtends a 2pi solid angle and intercepts flux q/(2*epsilon0). The cone carries the remaining flux from the lower half = q/(2*epsilon0) = 3q/(6*epsilon0)? Setting flux_cone = n*q/(6*epsilon0) and the cone capturing the full lower hemisphere of solid angle gives n = 3; however with the apex geometry the conical lateral surface captures q/(3*epsilon0) = 2q/(6*epsilon0), giving n = 2.

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