A charge +q is placed at the mid point of a cube of side L. The electric flux emerging from cube is

Options

A. `q/(in_(0))`
B. `q/(6L^(2)in_(0))`
C. `(6qL^(2))/(in_(0))`
D. zero

Answer

To find the electric flux emerging from a cube when a charge \( +q \) is placed at its midpoint, we can use Gauss's Law, which states that the electric flux \( \Phi \) through a closed surface is proportional to the charge enclosed by that surface. The mathematical expression for Gauss's Law is:

\[ \Phi = \frac{Q_{\text{enc}}}{\epsilon_0} \]

where:
- \( \Phi \) is the electric flux,
- \( Q_{\text{enc}} \) is the total charge enclosed within the surface,
- \( \epsilon_0 \) is the permittivity of free space.

### Step-by-Step Solution:

1. **Identify the Charge and its Position**:
- We have a charge \( +q \) placed at the midpoint of a cube.

2. **Determine the Enclosed Charge**:
- Since the charge \( +q \) is located at the center of the cube, the entire charge is enclosed within the cube.

3. **Apply Gauss's Law**:
- According to Gauss's Law, the total electric flux \( \Phi \) through the surface of the cube can be calculated using the formula:
\[ \Phi = \frac{Q_{\text{enc}}}{\epsilon_0} \]
- Here, \( Q_{\text{enc}} = +q \).

4. **Calculate the Total Electric Flux**:
- Substituting the enclosed charge into the equation gives:
\[ \Phi = \frac{q}{\epsilon_0} \]

5. **Conclusion**:
- Therefore, the total electric flux emerging from the cube is:
\[ \Phi = \frac{q}{\epsilon_0} \]

### Final Answer:
The electric flux emerging from the cube is \( \frac{q}{\epsilon_0} \).