Q.35 Physics ⭐ 360° Option Elimination Active

NEET 2025 Physics Question 35 Solution

Topic: Electric Charges and Fields · Official NTA Booklet Code 45

Question

An electric dipole with dipole moment 5×10⁻⁶ C m is aligned with the direction of a uniform electric field of magnitude 4×10⁵ N/C. The dipole is then rotated through an angle of 60° with respect to the electric field. The change in the potential energy of the dipole is:

✓

Verified Against NTA Final Answer Key

Option (2) : 1.0 J

📚 Electric Charges and Fields Easy

📋 Given Parameters & Problem Setup

Dipole Moment (p) 5 × 10⁻⁶ C·m

Electric Field Magnitude (E) 4 × 10⁵ N/C

Initial Orientation (θ₁) 0° (aligned with electric field)

Final Orientation (θ₂) 60°

⚡

The 30-Second Exam Hall Shortcut: ⚡ Dipole Potential Energy ΔU Shortcut

⏱️ Save ~30 seconds

ΔU = p E (cos θ₁ - cos θ₂) = p E (1 - cos 60°) = (p E) / 2 = [(5 × 10⁻⁶) × (4 × 10⁵)] / 2 = 2.0 / 2 = 1.0 J!

1 Potential energy of dipole in electric field: U(θ) = -p E cos θ.

2 Change in potential energy: ΔU = U(θ₂) - U(θ₁) = -p E cos 60° - (-p E cos 0°) = p E (cos 0° - cos 60°).

3 Evaluate cos values: cos 0° = 1, cos 60° = 0.5 ⟹ factor is (1 - 0.5) = 0.5.

4 Calculate product: p E = (5 × 10⁻⁶ C·m) × (4 × 10⁵ N/C) = 20 × 10⁻¹ = 2.0 J.

5 Multiply: ΔU = 0.5 × 2.0 J = 1.0 J.

6 Select Option (2) in under 10 seconds!

🛡️

Why You Can 100% Trust This Shortcut: Electrostatic Potential Energy of Electric Dipole (NCERT Physics · Electrostatic Potential: U = -p · E).

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Formula for Potential Energy of an Electric Dipole

The electrostatic potential energy U of an electric dipole with dipole moment p in a uniform electric field E is given by:

U(\theta) = -\vec{p} \cdot \vec{E} = -p E \cos\theta

• Stable equilibrium occurs at θ = 0° where U is minimum: U(0°) = -p E.

Step 2

Calculate Initial and Final Potential Energies

Evaluate U at initial angle θ₁ = 0° and final angle θ₂ = 60°:

U_1 = -p E \cos 0^\circ = -p E, \quad U_2 = -p E \cos 60^\circ = -\frac{1}{2} p E

• Change in potential energy is defined as ΔU = U₂ - U₁.

Step 3

Compute ΔU and Substitute Numerical Values

Calculate the difference and substitute p and E:

\Delta U = U_2 - U_1 = -\frac{1}{2} p E - (-p E) = \frac{1}{2} p E = \frac{1}{2} (5 \times 10^{-6}\text{ C}\cdot\text{m}) (4 \times 10^5\text{ N/C}) = \frac{1}{2} \times 2.0\text{ J} = 1.0\text{ J}

• Matches Option (2) with complete precision.

⭐

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 A

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. Arises from using cos 37° = 0.8 or sin function.

⚠️

Student Fallacy (Why candidates pick this trap): Using torque formula τ = p E sin θ instead of work/energy formula.

2 B

✓ 100% Correct

Verdict & Scientific Reason:

100% correct. ΔU = p E (1 - cos 60°) = 2.0 × 0.5 = 1.0 J.

💡

Why this is airtight: None; direct application of dipole potential energy formula.

3 C

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. Arbitrary distractor.

⚠️

Student Fallacy (Why candidates pick this trap): Arithmetic slip in evaluating p E.

4 D

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. Corresponds to rotation to 120°: p E (1 - cos 120°) = 2.0 × 1.5 / 2 = 1.5 J.

⚠️

Student Fallacy (Why candidates pick this trap): Using 120° angle instead of 60°.

⚠️

NTA Trap Alert: Confusing Torque with Work/Energy (sin θ vs. cos θ)

Torque on a dipole is τ = p E sin θ, whereas potential energy is U = -p E cos θ. Using sin θ yields p E sin 60° = 2 × (√3/2) = √3 ≈ 1.732 J.

🛡️ How to avoid the -1 mark: Always remember: Work/Energy uses COSINE; Torque uses SINE.

📖

Core NEET Syllabus Standard

NEET Physics Core Syllabus · Electric Charges and Fields Standard Benchmark

Core Scientific Principle Tested:

"ΔU = W_{ext} = p E (cos θ₁ - cos θ₂)."

Syllabus Focus: Dipole in a Uniform External Field

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

ΔU = p E (1 - cos 60°) = 2.0 × (1/2) = 1.0 J!

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NEET 2025 Physics Question 35 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Dipole Potential Energy ΔU Shortcut

Step-by-Step Rigorous Workflow & Mathematical Proof

Formula for Potential Energy of an Electric Dipole

Calculate Initial and Final Potential Energies

Compute ΔU and Substitute Numerical Values

360° Option Elimination Engine Key Feature

NTA Trap Alert: Confusing Torque with Work/Energy (sin θ vs. cos θ)

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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