Net flux linked to a closed surface around a charged particle is …….. Times the charge.

Options

A. `epsilon_0`
B. `1/(epsilon_0)`
C. `epsilon_0^2`
D. None of these

Answer

To solve the question regarding the net flux linked to a closed surface around a charged particle, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Gauss's Law**: Gauss's Law states that the electric flux (\( \Phi \)) through a closed surface is directly proportional to the net charge (\( Q \)) enclosed within that surface. The mathematical expression for Gauss's Law is given by:
\[ \Phi = \frac{Q}{\varepsilon_0} \]
where \( \varepsilon_0 \) is the permittivity of free space.

2. **Identify the Charge**: In this scenario, we have a charged particle with charge \( +q \). This charge is enclosed by a closed surface (Gaussian surface).

3. **Apply Gauss's Law**: According to Gauss's Law, the net flux linked to the closed surface surrounding the charge \( +q \) can be expressed as:
\[ \Phi = \frac{q}{\varepsilon_0} \]

4. **Relate Flux to Charge**: The question asks how many times the charge \( q \) is represented in the expression for the flux. From the equation derived from Gauss's Law, we can see that:
\[ \Phi = \frac{q}{\varepsilon_0} = \left(\frac{1}{\varepsilon_0}\right) \times q \]
This indicates that the net flux linked to the closed surface is \( \frac{1}{\varepsilon_0} \) times the charge \( q \).

5. **Conclusion**: Therefore, the net flux linked to a closed surface around a charged particle is \( \frac{1}{\varepsilon_0} \) times the charge.

### Final Answer:
The net flux linked to a closed surface around a charged particle is \( \frac{1}{\varepsilon_0} \) times the charge.

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