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According to Gauss's theorem, electric flux through a closed surface = Q / ε₀ where q is charge enclosed by the surface. The charge is kept at a corner of a cube so it can be visualised as being at the centre of 8 cubes. Find flux through each cube.

1. ϕ = q / ε₀
2. ϕ = q / 6ε₀
3. ϕ = q / 8ε₀
4. ϕ = q / 12ε₀

Correct answer: ϕ = q / 8ε₀

Solution

The charge is at the corner of a cube, and it can be considered as shared by 8 cubes. By symmetry, the flux through each cube is 1/8th of the total flux, which is q/ε₀. Therefore, the flux through each cube is q/8ε₀.

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