Question:
Electric flux through a closed surface depends on
Electric flux through a closed surface depends on
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Gauss's Law is powerful because of its simplicity. Remember: Net Flux = (Net Enclosed Charge) / $\epsilon_0$. Shape, size, and external charges are irrelevant to the \textbf{net total} flux.
Updated On: Apr 21, 2026
- Area of flux
- Volume
- Charge enclosed
- Shape
- Electric field outside it
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The Correct Option is C
Solution and Explanation
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:
\[ \Phi_E = \oint \mathbf{E} \cdot d\mathbf{A} = \frac{Q_{enclosed}}{\epsilon_0} \]
Where:
\(\Phi_E\) = Total electric flux through a closed surface
\(Q_{enclosed}\) = Net charge enclosed by the surface
\(\epsilon_0\) = Vacuum permittivity
Step 3: Detailed Explanation:
Looking at the formula for Gauss's Law, the total electric flux \(\Phi_E\) through \textit{any} closed Gaussian surface is entirely determined by the net charge enclosed (\(Q_{enclosed}\)) divided by a constant (\(\epsilon_0\)).
- 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.
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:
\[ \Phi_E = \oint \mathbf{E} \cdot d\mathbf{A} = \frac{Q_{enclosed}}{\epsilon_0} \]
Where:
\(\Phi_E\) = Total electric flux through a closed surface
\(Q_{enclosed}\) = Net charge enclosed by the surface
\(\epsilon_0\) = Vacuum permittivity
Step 3: Detailed Explanation:
Looking at the formula for Gauss's Law, the total electric flux \(\Phi_E\) through \textit{any} closed Gaussian surface is entirely determined by the net charge enclosed (\(Q_{enclosed}\)) divided by a constant (\(\epsilon_0\)).
- 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.
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