Q.26 Physics ⭐ 360° Option Elimination Active
NEET 2023 Physics Question 26 Solution
Topic: Electric Charges and Fields · Official NTA Booklet Code G5
Question
If ∮ E · dS = 0 over a surface, then:
✓
Verified Against NTA Final Answer Key
Option (2) : the net charge within the surface is zero
📚 Electric Charges and Fields Easy
📋 Given Parameters & Problem Setup
Surface condition Closed surface in vacuum
Electric field lines entering Equal to electric field lines leaving
Net electric flux (Φ_net) 0
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⏱️ Save ~45 seconds The 30-Second Exam Hall Shortcut: ⚡ Gauss’s Law Net Flux Principle: Φ_net = q_enc / ε₀
Number of lines entering = Number of lines leaving ⟹ Net flux Φ_net = 0 ⟹ Net enclosed charge q_enc = 0 in 5 seconds!
1 Electric flux represents the net count of electric field lines crossing a closed surface.
2 Lines entering count as negative flux; lines exiting count as positive flux.
3 If entering lines equal exiting lines, net electric flux Φ_net = 0.
4 By Gauss’s Law, Φ_net = q_enc / ε₀.
5 Since Φ_net = 0, the net enclosed charge q_enc must be identically zero.
6 Directly select Option (2)!
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Why You Can 100% Trust This Shortcut: Fundamental Electrostatics · Gauss’s Law (Net flux through any closed Gaussian surface equals net enclosed charge divided by permittivity of free space).
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Step-by-Step Rigorous Workflow & Mathematical Proof
Step 1
Definition of Electric Flux in Terms of Field Lines
The electric flux Φ through a closed Gaussian surface S is geometrically defined as the net count of electric field lines penetrating the surface. Inward-directed lines contribute negative flux, while outward-directed lines contribute positive flux:
Step 2
Application of Given Equal-Line Condition
The problem states that the number of field lines entering the closed surface equals the number of field lines leaving it. Therefore:
Step 3
Application of Gauss’s Law
According to Gauss’s Law of electrostatics, the net electric flux through any closed Gaussian surface in vacuum is directly proportional to the total net charge q_enc enclosed within the surface:
Step 4
Conclusion on Enclosed Charge
Equating the net flux to zero yields:
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4-Option Deep Scan
360° Option Elimination Engine Key Feature
Diagnose every choice: Know exactly why the right option works and why distractors fail.
1 (1)
✗ Incorrect Verdict & Scientific Reason:
Uniform electric field is neither necessary nor implied; non-uniform external fields also produce zero net flux.
⚠️
Student Fallacy (Why candidates pick this trap): Candidate confused zero divergence/net flux with spatial uniformity of the field.
2 (2)
✓ 100% Correct Verdict & Scientific Reason:
Accurate deduction from Gauss’s Law: zero net flux guarantees zero net enclosed charge.
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Why this is airtight: None. Candidate correctly applied Gauss’s Law.
3 (3)
✗ Incorrect Verdict & Scientific Reason:
External charges can exist freely; all field lines from external charges that enter the surface must also exit.
⚠️
Student Fallacy (Why candidates pick this trap): Candidate forgot that external charges produce equal entering and leaving flux lines.
4 (4)
✗ Incorrect Verdict & Scientific Reason:
Completely unphysical and baseless claim.
⚠️
Student Fallacy (Why candidates pick this trap): Wild guess with no physical basis.
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NTA Trap Alert: Confusing "Net Charge Zero" with "Zero Electric Field"
Zero net flux (Φ = 0) means the algebraic SUM of enclosed charges is zero (e.g., an electric dipole inside has q_net = 0). It does NOT mean the electric field E is zero everywhere on the surface, nor does it mean no field lines exist.
🛡️ How to avoid the -1 mark: Remember: Gauss’s Law links NET FLUX to NET ENCLOSED CHARGE: Φ = ∮ E · dA = q_net / ε₀.
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Core NEET Syllabus Standard
National Eligibility cum Entrance Test (NEET UG) · Electric Charges and Fields Standard Benchmark
Core Scientific Principle Tested:
"The total electric flux through a closed surface is equal to 1/ε₀ times the total charge enclosed within the surface."
Syllabus Focus: Gauss’s Law and Surface Flux
Preserved in Rationalized Curriculum Syllabus & Academic Standards ↗
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