Gauss's Law

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A charge Q is placed at the center of a cube. What is the electric flux through one face of the cube?

RankGuru · Accepted Answer

1. **Gauss's Law**: The total flux through a closed surface is $\Phi_{total} = Q_{net}/\epsilon_0$.
2. **Identify Surface**: The cube is a closed symmetric surface enclosing the charge $Q$.
3. **Distribute Flux**: A cube has 6 identical faces. Since the charge is exactly at the center, the flux passes through each face equally (symmetrically).
4. **Calculate per Face**:
   - $\Phi_{face} = \frac{1}{6} \Phi_{total} = \frac{Q}{6\epsilon_0}$.
5. **Inference**: If the charge was on a corner, we would need 8 cubes to enclose it, resulting in a different distribution.

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