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Flux through all six faces as per Gauss's theorem should be q / ε₀. Find flux coming out of each face.

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

Correct answer: ϕ = q / 6ε₀

Solution

According to Gauss's theorem, the total flux through a closed surface is q/ε₀. For a cube with a charge at its center, the flux is uniformly distributed across all six faces. Thus, the flux through each face is (q/ε₀)/6 = q/6ε₀.

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