Question

What is the value of total electric flux coming out of a closed surface?

• A. Zero
• B. Equal to volume charge density
• C. Equal to the total charge enclosed by the surface
• D. Equal to the surface charge density

Hint:

Gauss’s Law is valid for all closed surfaces, even irregular ones. Always focus on charges *inside* the surface.

Answer 1

The Correct Option is C

Step 1: Recall Gauss’s Law.
Gauss’s Law is one of Maxwell’s equations in electrostatics. It states: \[ \Phi_E = \oint_S \vec{E} \cdot d\vec{A} = \frac{Q_{\text{enclosed}}}{\varepsilon_0} \] Where:
- $\Phi_E$ is the total electric flux through a closed surface,
- $Q_{\text{enclosed}}$ is the total charge enclosed within the surface,
- $\varepsilon_0$ is the vacuum permittivity.
Step 2: Interpret the meaning.
The flux depends only on the net charge enclosed inside the surface, irrespective of how that charge is distributed or whether there are external charges nearby. This is a key concept that simplifies electrostatics analysis.
Conclusion: Total electric flux out of a closed surface is: \[ \boxed{\text{Equal to the total charge enclosed by the surface}} \]