Q.29 Physics · Section A ⭐ 360° Option Elimination Active

NEET 2024 Physics Question 29 Solution

Topic: Electric Charges and Fields · Official NTA Booklet Code T1

Question

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R: Assertion A: The potential (V) at any axial point, at 2 m distance (r) from the centre of the dipole of dipole moment vector P of magnitude, 4×10⁻⁶ C m, is ±9×10³ V. (Take 1/(4πε₀) = 9×10⁹ SI units) Reason R: V = ±2P/(4πε₀r²), where r is the distance of any axial point, situated at 2 m from the centre of the dipole. In the light of the above statements, choose the correct answer from the options given below:

✓

Verified Against NTA Final Answer Key

Option (1) : A is true but R is false.

📚 Electric Charges and Fields Easy

📋 Given Parameters & Problem Setup

Distance from dipole center r = 2 m

Dipole moment magnitude P = 4 × 10⁻⁶ C m

Coulomb constant 1 / (4πε₀) = 9 × 10⁹ SI units

Assertion A Potential V at axial point at 2 m is ±9 × 10³ V

Reason R Formula given as V = ± (2P) / (4πε₀ r²)

⚡

The 30-Second Exam Hall Shortcut: ⚡ Formula Discrepancy Spotter

⏱️ Save ~40 seconds

Electric FIELD has 2P (E = 2kp/r³), but electric POTENTIAL has only P (V = kp/r²)! Reason R has false 2P -> R is FALSE -> Instant Option (1)!

1 Recall dipole potential on axial line: V = ± P / (4πε₀ r²). Notice there is NO factor of 2!

2 Calculate V: V = ± (9 × 10⁹) × (4 × 10⁻⁶) / 2² = ± (36 × 10³) / 4 = ± 9 × 10³ V -> Assertion A is TRUE.

3 Inspect Reason R: R states V = ± 2P / (4πε₀ r²). This equation is mathematically FALSE (the factor of 2 belongs to electric FIELD E, not potential V).

4 Thus, A is true but R is false.

5 Option (1) in under 10 seconds!

🛡️

Why You Can 100% Trust This Shortcut: NCERT Physics · Electrostatic Potential and Capacitance (Electric potential of a dipole: V = p cos θ / (4πε₀ r²)).

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Evaluation of Assertion A (Numerical Value)

The electrostatic potential due to a short electric dipole of dipole moment P at a distance r along its axial line is given by:

V = \pm \frac{1}{4\pi\varepsilon_0} \frac{P}{r^2}

Step 2

Substitution into Potential Formula

Substitute 1/(4πε₀) = 9 × 10⁹ N m²/C², P = 4 × 10⁻⁶ C m, and r = 2 m:

V = \pm (9 \times 10^9) \frac{4 \times 10^{-6}}{2^2} = \pm (9 \times 10^9) \frac{4 \times 10^{-6}}{4} = \pm 9 \times 10^3\,\text{V}

Step 3

Verdict for Assertion A

The calculated potential matches ±9 × 10³ V exactly. Therefore, Assertion A is completely TRUE.

\text{Assertion A is True}

Step 4

Evaluation of Reason R (Formula Validity)

Reason R claims that the potential formula is V = ± (2P) / (4πε₀ r²). This is scientifically incorrect. The factor of 2 appears in the axial electric field formula E = 2P / (4πε₀ r³), but NOT in the potential formula V = P / (4πε₀ r²). Therefore, Reason R is FALSE.

V_{axial} = \pm \frac{P}{4\pi\varepsilon_0 r^2} \ne \pm \frac{2P}{4\pi\varepsilon_0 r^2} \implies \text{Reason R is False}

⭐

360° Option Elimination Engine Key Feature

Diagnose every choice: Know exactly why the right option works and why distractors fail.

4-Option Deep Scan

1 (1)

✓ 100% Correct

Verdict & Scientific Reason:

Assertion is numerically accurate; Reason contains a false formula with an extraneous factor of 2.

💡

Why this is airtight: None.

2 (2)

✗ Incorrect

Verdict & Scientific Reason:

Inverts both truths.

⚠️

Student Fallacy (Why candidates pick this trap): Accepting the false formula in R and rejecting the correct calculation in A.

3 (3)

✗ Incorrect

Verdict & Scientific Reason:

Reason is fundamentally false.

⚠️

Student Fallacy (Why candidates pick this trap): Failing to notice the extra factor of 2 in Reason R.

4 (4)

✗ Incorrect

Verdict & Scientific Reason:

Reason is false.

⚠️

Student Fallacy (Why candidates pick this trap): Believing R is true.

⚠️

NTA Trap Alert: Confusing Dipole Electric Field (2P) with Potential (P)

NTA intentionally inserted the factor of 2 into Reason R because students often conflate E_axial = 2kp/r³ with V_axial = kp/r².

🛡️ How to avoid the -1 mark: Potential is scalar work: V = kp cos θ / r² (no factor of 2!). Field is vector derivative: E = 2kp / r³ (has factor of 2!).

📖

Core NEET Syllabus Standard

Physics Core Electrostatics · Electric Charges and Fields Standard Benchmark

Core Scientific Principle Tested:

"The electric potential at an axial point of a dipole is V = ± P / (4πε₀ r²), decaying as 1/r² without any factor of 2."

Syllabus Focus: Electric Dipole in Electrostatics

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

Field gets the Factor of Two; Potential has only P for you!

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NEET 2024 Physics Question 29 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Formula Discrepancy Spotter

Step-by-Step Rigorous Workflow & Mathematical Proof

Evaluation of Assertion A (Numerical Value)

Substitution into Potential Formula

Verdict for Assertion A

Evaluation of Reason R (Formula Validity)

360° Option Elimination Engine Key Feature

NTA Trap Alert: Confusing Dipole Electric Field (2P) with Potential (P)

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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