A point charge is placed at the midpoint of an edge of cube. How much electric flux will be associated with the cube?

Options

A. `q//epsilon_0`
B. `q//2epsilon_0`
C. `q//8epsilon_0`
D. `q//4epsilon_0`

Explanation

To find the electric flux associated with a cube when a point charge \( Q \) is placed at the midpoint of one of its edges, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Configuration**:
- We have a cube and a point charge \( Q \) placed at the midpoint of one of its edges.

2. **Identifying the Enclosed Charge**:
- The charge \( Q \) is not fully enclosed by the cube. To determine the total electric flux through the cube, we need to consider how many cubes would be needed to completely enclose the charge \( Q \).

3. **Visualizing the Symmetry**:
- The charge \( Q \) at the midpoint of the edge is symmetrically located with respect to the surrounding space. If we visualize the arrangement, we can see that the charge \( Q \) would be shared among multiple cubes.

4. **Calculating the Number of Cubes**:
- Since the charge is at the midpoint of an edge, it can be thought of as being shared equally by four cubes that would surround it. Thus, the number of cubes that would completely enclose the charge \( Q \) is 4.

5. **Applying Gauss's Law**:
- According to Gauss's Law, the total electric flux \( \Phi \) through a closed surface is given by:
\[ \Phi = \frac{Q_{\text{enc}}}{\epsilon_0} \]
- In this case, since the charge \( Q \) is shared by 4 cubes, the total flux through all 4 cubes is:
\[ \Phi_{\text{total}} = \frac{Q}{\epsilon_0} \]

6. **Finding the Flux Through One Cube**:
- Since the total flux is distributed equally among the 4 cubes, the electric flux through one cube is:
\[ \Phi_{\text{one cube}} = \frac{1}{4} \cdot \Phi_{\text{total}} = \frac{1}{4} \cdot \frac{Q}{\epsilon_0} = \frac{Q}{4\epsilon_0} \]

7. **Final Answer**:
- Therefore, the electric flux associated with the cube is:
\[ \Phi = \frac{Q}{4\epsilon_0} \]