Q.25 Physics ⭐ 360° Option Elimination Active

NEET 2023 Physics Question 25 Solution

Topic: Electric Charges and Fields · Official NTA Booklet Code G5

Question

An electric dipole is placed at an angle of 30° with an electric field of intensity 2×10⁵ N C⁻¹. It experiences a torque equal to 4 N m. Calculate the magnitude of charge on the dipole, if the dipole length is 2 cm.

✓

Verified Against NTA Final Answer Key

Option (1) : 2 mC

📚 Electric Charges and Fields Easy

📋 Given Parameters & Problem Setup

Angle with field (θ) 30°

Electric Field (E) 2 × 10⁵ N/C

Experienced Torque (τ) 4 N m

Dipole Length (2a) 2 cm = 2 × 10⁻² m

⚡

The 30-Second Exam Hall Shortcut: ⚡ Torque Formula τ = q (2a) E sin θ Direct Cancellation

⏱️ Save ~40 seconds

4 = q × (2 × 10⁻²) × (2 × 10⁵) × sin 30° = q × 2000! Thus q = 4 / 2000 = 2 × 10⁻³ C = 2 mC in 15 seconds!

1 Recall torque on a dipole: τ = p E sin θ = q (2a) E sin θ.

2 Substitute given values: 4 = q × (2 × 10⁻² m) × (2 × 10⁵ N/C) × (1/2).

3 Notice the 2 in length cancels with 1/2 from sin 30°: (2 × 10⁻²) × (1/2) = 10⁻².

4 Multiply by E: 10⁻² × (2 × 10⁵) = 2 × 10³ = 2000.

5 Solve for q: q = 4 / 2000 = 2 × 10⁻³ C = 2 mC.

6 Lock Option (1) 2 mC with 100% confidence!

🛡️

Why You Can 100% Trust This Shortcut: Fundamental Electrostatics · Dipole Mechanics (Torque relation: τ⃗ = p⃗ × E⃗ → τ = q · 2a · E · sin θ).

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Governing Formula for Torque on an Electric Dipole

When an electric dipole of dipole moment p⃗ = q(2a⃗) is placed in a uniform electric field E⃗ at an angle θ, it experiences a restoring torque given by the vector cross product:

\tau = p E \sin\theta = q (2a) E \sin\theta

Step 2

Substitution of Given Physical Quantities

Substitute torque τ = 4 N m, length 2a = 2 × 10⁻² m, electric field E = 2 × 10⁵ N/C, and angle θ = 30°:

4 = q \times (2 \times 10^{-2}) \times (2 \times 10^5) \times \sin 30^\circ

Step 3

Simplification and Isolation of Charge q

Evaluate the trigonometric and metric terms using sin 30° = 1/2:

4 = q \times (2 \times 10^{-2}) \times (2 \times 10^5) \times \frac{1}{2} = q \times (2 \times 10^3) = 2000 q

Step 4

Charge Evaluation in Millicoulombs

Solve for charge q and express in millicoulombs (1 mC = 10⁻³ C):

q = \frac{4}{2000} = 2 \times 10^{-3}\text{ C} = 2\text{ mC}

⭐

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:

Accurate charge magnitude matching NTA final answer key and torque derivation.

💡

Why this is airtight: None. Candidate executed the cancellation of factors accurately.

2 (2)

✗ Incorrect

Verdict & Scientific Reason:

Overestimates charge by a factor of 4.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate multiplied by 2 instead of dividing by sin 30°.

3 (3)

✗ Incorrect

Verdict & Scientific Reason:

Arbitrary arithmetic slip.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate added numbers in the numerator.

4 (4)

✗ Incorrect

Verdict & Scientific Reason:

Forgot the factor of 2 in the denominator.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate forgot the 2 from 2 × 10⁵ or cancelled the 2 in the numerator improperly, obtaining q = 4 / 1000 = 4 mC.

⚠️

NTA Trap Alert: Cancelling the Wrong Factor of 2 (Leading to 4 mC)

A student who writes 4 = q × (10⁻²) × (2 × 10⁵) × (0.5) might cancel the 2 with 0.5 without accounting for the 2 in 2 cm length, obtaining q = 4 / 1000 = 4 mC (Option 4).

🛡️ How to avoid the -1 mark: Keep track of both factors: Dipole length is 2 cm = 2 × 10⁻² m; Electric field is 2 × 10⁵ N/C; sin 30° is 1/2.

📖

Core NEET Syllabus Standard

National Eligibility cum Entrance Test (NEET UG) · Electric Charges and Fields Standard Benchmark

Core Scientific Principle Tested:

"Torque on a dipole is τ = p E sin θ. Dipole moment is charge times full separation (p = q × 2a)."

Syllabus Focus: Electric Dipole in a Uniform External Field

Preserved in Rationalized Curriculum Syllabus & Academic Standards ↗

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NEET 2023 Physics Question 25 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Torque Formula τ = q (2a) E sin θ Direct Cancellation

Step-by-Step Rigorous Workflow & Mathematical Proof

Governing Formula for Torque on an Electric Dipole

Substitution of Given Physical Quantities

Simplification and Isolation of Charge q

Charge Evaluation in Millicoulombs

360° Option Elimination Engine Key Feature

NTA Trap Alert: Cancelling the Wrong Factor of 2 (Leading to 4 mC)

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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