Gauss Law

Step 1:
In electrostatic equilibrium, electric field inside a conductor is .


Step 2:
For an empty cavity inside a conductor with no charge inside, in the cavity.


Step 3:
Since , potential remains constant inside the cavity.


Step 4:
The constant potential inside the cavity is equal to the surface potential of the conductor, hence .
Final Answer:
Option D: .

Concept:

Step 1: Net flux.


Step 2: Gauss law.

According to Gauss’s law: So electric flux through a closed surface depends only on the net charge enclosed by the surface. It does not depend on:

• shape of the surface,
• area of the surface,
• volume of the surface,
• electric field due to outside charges.

Hence, the correct answer is:

Step 1: Understanding the Concept:
This question directly tests the conceptual understanding of Gauss's Law in electrostatics. Gauss's Law relates the total electric flux passing through a closed surface to the electric charge contained within that surface.
Step 2: Key Formula or Approach:
Gauss's Law is stated mathematically as:

Where:
= Total electric flux through a closed surface
= Net charge enclosed by the surface
= Vacuum permittivity
Step 3: Detailed Explanation:
Looking at the formula for Gauss's Law, the total electric flux through \textit{any} closed Gaussian surface is entirely determined by the net charge enclosed ( ) divided by a constant ( ).
- It does not depend on the total area or volume of the surface.
- It does not depend on the geometric shape of the closed surface (whether it's a sphere, cube, or an irregular blob).
- It does not depend on the spatial distribution of the charges \textit{inside} the surface, only their net algebraic sum.
- Charges placed \textit{outside} the closed surface contribute zero net flux through the surface (flux entering equals flux exiting).
Therefore, the only variable factor among the choices is the charge enclosed.
Step 4: Final Answer:
Electric flux through a closed surface depends on the charge enclosed.