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Question 31431
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Electrostatics: Gauss's Law MCQ

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Gauss's LawHardQuestion 31431

Question

A point charge +q is placed at one corner of a cube of side L. Flux through one face not adjacent to the charge:
  1. A
    q/(24ε₀)
    Correct
  2. B
    q/(6ε₀)
  3. C
    q/(12ε₀)
  4. D
    q/(48ε₀)

Correct answer

q/(24ε₀)

Explanation

Use 8-cube argument: +q at corner means 8 identical cubes share this corner. Total flux from 8 cubes = q/ε₀. Each cube gets q/(8ε₀). Cube has 3 faces adjacent to charge (zero flux by symmetry) and 3 non-adjacent. By symmetry, each non-adjacent face gets q/(8ε₀)/3 = q/(24ε₀).

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