Electric Flux

Question

A charge q is placed at the center of a cube of side a. The electric flux passing through one face of the cube is:

RankGuru · Accepted Answer

1. **Gauss's Law**: The total electric flux through any closed surface is $\Phi_{total} = \frac{q_{enclosed}}{\epsilon_0}$.
2. **Symmetry Argument**: For a point charge at the center of a cube, the flux is equally shared by the 6 symmetric faces.
3. **Calculation**: Flux through one face $\Phi_{face} = \frac{1}{6} \Phi_{total} = \frac{1}{6} 	imes \frac{q}{\epsilon_0}$.
4. **Result**: The flux is $\frac{q}{6\epsilon_0}$.

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Electric Flux

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