A charge q is inside a closed surface and charge -q is outside. The out going electric flux is

Options

A. `-q//in_(0)`
B. zero
C. `q//in_(0)`
D. `2q//in_(0)`

Answer

To solve the problem of finding the outgoing electric flux when a charge \( q \) is inside a closed surface and a charge \( -q \) is outside, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Electric Flux**:
Electric flux (\( \Phi_E \)) through a closed surface is defined by Gauss's Law, which states that the electric flux through a closed surface is proportional to the net charge enclosed within that surface. Mathematically, it is given by:
\[ \Phi_E = \frac{Q_{\text{enc}}}{\epsilon_0} \]
where \( Q_{\text{enc}} \) is the total charge enclosed by the surface and \( \epsilon_0 \) is the permittivity of free space.

2. **Identify the Charges**:
In this scenario, we have:
- A charge \( q \) inside the closed surface.
- A charge \( -q \) outside the closed surface.

3. **Determine the Enclosed Charge**:
Since the charge \( -q \) is outside the closed surface, it does not contribute to the electric flux through the surface. Therefore, the only charge that contributes to the electric flux is the charge \( q \) that is inside the surface.

4. **Apply Gauss's Law**:
According to Gauss's Law, we can calculate the electric flux through the closed surface as follows:
\[ \Phi_E = \frac{q}{\epsilon_0} \]

5. **Final Result**:
The outgoing electric flux through the closed surface is:
\[ \Phi_E = \frac{q}{\epsilon_0} \]