In a uniform electric field E if we consider an imaginary cubical closed surface of side a, then find the net flux through the cube ?

Answer

To find the net electric flux through a cubical closed surface in a uniform electric field, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**: We have a uniform electric field \( E \) and a cube with side length \( a \). We need to find the net electric flux through the cube.

2. **Visualizing the Cube**: Draw an imaginary cube. The cube has six faces, and we need to consider the electric field lines that pass through each face.

3. **Applying Gauss's Law**: According to Gauss's Law, the electric flux \( \Phi \) through a closed surface is given by:
\[ \Phi = \frac{Q_{\text{enc}}}{\epsilon_0} \]
where \( Q_{\text{enc}} \) is the charge enclosed within the surface, and \( \epsilon_0 \) is the permittivity of free space.

4. **Identifying Charge Enclosed**: In this case, since the cube is empty (no charge is enclosed within it), we have:
\[ Q_{\text{enc}} = 0 \]

5. **Calculating the Net Flux**: Substituting \( Q_{\text{enc}} = 0 \) into Gauss's Law gives:
\[ \Phi = \frac{0}{\epsilon_0} = 0 \]

6. **Conclusion**: Therefore, the net electric flux through the cube is:
\[ \Phi = 0 \]

### Final Answer:
The net flux through the cube is \( 0 \).

---