A charge Q is situated at the corner of a cube, the electric flux passing through all the six faces of the cube is :

Options

A. `(Q)/(24epsilon_(0))`
B. `(Q)/(3epsilon_(0))`
C. `(Q)/(8epsilon_(0))`
D. `(Q)/(6epsilon_(0))`

Answer

To find the electric flux passing through all six faces of a cube when a charge \( Q \) is situated at one corner, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Setup**:
- A charge \( Q \) is placed at one corner of a cube.
- This corner is shared by eight adjacent cubes.

2. **Determining the Contribution of Charge**:
- Since the charge is at the corner, it contributes to the electric flux through the faces of the cube.
- The charge \( Q \) is effectively shared among eight cubes. Therefore, the portion of the charge contributing to the flux through this particular cube is:
\[ Q_{\text{enclosed}} = \frac{Q}{8} \]

3. **Applying Gauss's Law**:
- Gauss's Law states that the total electric flux \( \Phi \) through a closed surface is proportional to the enclosed charge:
\[ \Phi = \frac{Q_{\text{enclosed}}}{\epsilon_0} \]
- Substituting the enclosed charge:
\[ \Phi = \frac{Q/8}{\epsilon_0} = \frac{Q}{8\epsilon_0} \]

4. **Final Result**:
- Therefore, the electric flux passing through all six faces of the cube is:
\[ \Phi = \frac{Q}{8\epsilon_0} \]

### Conclusion:
The electric flux through all six faces of the cube is \( \frac{Q}{8\epsilon_0} \).

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