The Question is from neet-physics electrostatic-charges-and-fields electric-flux-and-gauss-law, and it was created by the author Mr. ANIL KUMAR.G

Question

A spherical Gaussian surface encloses a point charge $q$. If the radius of the sphere is doubled, the electric flux through the surface will:

Mr. ANIL KUMAR.G · Accepted Answer

## CORE INFORMATION
✓ **Answer**: D
## CONCEPT FRAMEWORK
 **Primary Concept**: Gauss's Law
 **Related Topics**: Electric Flux, Electric Field, Point Charge
 **Prerequisites**: Understanding of Gauss's Law and its application to spherical symmetry.
## SOLUTION PATHWAY
**Given Information**:
  A spherical Gaussian surface encloses a point charge $q$.
  The radius of the sphere is doubled.
**Method & Steps**:
 1. Apply Gauss's Law:
  Reasoning: Gauss's Law states that the total electric flux ($\Phi$) through a closed surface is equal to the enclosed charge ($q$) divided by the permittivity of free space ($\epsilon_0$).
  Formula/Rule: $\Phi = \frac{q}{\epsilon_0}$
 2. Analyze the effect of doubling the radius:
  Working: The electric flux depends only on the enclosed charge ($q$) and the permittivity of free space ($\epsilon_0$). Doubling the radius of the Gaussian sphere does not change the enclosed charge. Therefore, the electric flux remains the same.
  Key Point: The radius of the Gaussian surface does not affect the electric flux as long as the enclosed charge remains constant.
 3. Final Conclusion:
  Result: The electric flux through the surface will remain the same.
  Verification: The formula $\Phi = \frac{q}{\epsilon_0}$ shows no dependence on the radius of the Gaussian surface.
 ## OPTION ANALYSIS
A :x: Doubling the radius does not double the flux according to Gauss's law.
B :x: Doubling the radius does not halve the flux according to Gauss's law.
C :x: Doubling the radius does not quadruple the flux according to Gauss's law.
D ✓: The electric flux remains the same because it only depends on the enclosed charge, which is unchanged.
 ## LEARNING AIDS
 **Common Mistakes**:
  1.Confusing electric flux with electric field: The electric field strength decreases with the square of the distance from the point charge, but the total flux remains constant.
  How to avoid: Remember Gauss's law focuses on the total flux, not the field strength at a particular point.
  2.Assuming the flux depends on the surface area: While the surface area changes, the total flux remains constant due to the inverse relationship between the electric field and the distance from the charge.
  How to avoid: Carefully consider the implications of Gauss's Law and the relationship between flux, charge, and permittivity.
 **Quick Tips**:
  1.For a point charge enclosed by a spherical Gaussian surface, the electric flux is always $\frac{q}{\epsilon_0}$, regardless of the radius.
  2.Visualize the electric field lines emanating from the point charge. The number of field lines passing through the surface represents the flux, which remains constant even if the surface area changes.

Mr. ANIL KUMAR.G · Answer

Become double

Mr. ANIL KUMAR.G · Answer

Become half

Mr. ANIL KUMAR.G · Answer

Become four times

Mr. ANIL KUMAR.G · Answer

The correct Option is "Remain the same"

NEET Physics Electrostatic Charges and Fields Electric Flux And Gauss Law MCQs

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