Q.12 Physics ⭐ 360° Option Elimination Active

NEET 2025 Physics Question 12 Solution

Topic: Moving Charges and Magnetism · Official NTA Booklet Code 45

Question

A 2 amp current is flowing through two different small circular copper coils having radii ratio 1:2. The ratio of their respective magnetic moments will be

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Verified Against NTA Final Answer Key

Option (1) : 1:4

📚 Moving Charges and Magnetism Easy

📋 Given Parameters & Problem Setup

Current in Coils (I) 2 A (identical for both coils)

Radii Ratio (r₁ : r₂) 1 : 2

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The 30-Second Exam Hall Shortcut: ⚡ Area Scaling M ∝ r² Rule

⏱️ Save ~30 seconds

Magnetic Moment M = I · A = I (π r²) ⟹ M ∝ r² ⟹ M₁ / M₂ = (1/2)² = 1/4 = 1:4!

1 Recall formula: Magnetic dipole moment of a flat circular loop is M = I A.

2 Area of circle is A = π r².

3 Since current I is identical (2 A for both): M ∝ r².

4 Ratio: M₁ / M₂ = (r₁ / r₂)² = (1 / 2)² = 1 / 4.

5 Select Option (1) in under 5 seconds!

🛡️

Why You Can 100% Trust This Shortcut: Ampère’s Force Law (NCERT Physics · Moving Charges and Magnetism: F/L = μ₀ I₁ I₂ / (2πd)).

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Formula for Magnetic Dipole Moment

The magnetic dipole moment M of a planar loop of area A carrying current I is defined as:

M = I \vec{A} \implies M = I (\pi r^2)

• M is directly proportional to the enclosed area.

Step 2

Ratio Calculation

For two circular coils carrying the same current I = 2 A with radii r₁ and r₂:

\frac{M_1}{M_2} = \frac{I \pi r_1^2}{I \pi r_2^2} = \left(\frac{r_1}{r_2}\right)^2 = \left(\frac{1}{2}\right)^2 = \frac{1}{4}

• Thus the ratio of their respective magnetic moments is 1:4.

⭐

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

✓ 100% Correct

Verdict & Scientific Reason:

100% correct. M ∝ r² ⟹ (1/2)² = 1/4 = 1:4.

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Why this is airtight: None; direct quadratic scaling.

2 B

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. Linear ratio r₁:r₂, forgetting that area depends on the square of the radius.

⚠️

Student Fallacy (Why candidates pick this trap): Assuming magnetic moment scales linearly with radius.

3 C

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. Inverted linear ratio.

⚠️

Student Fallacy (Why candidates pick this trap): Inverting ratio and forgetting square.

4 D

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. Inverted quadratic ratio (M₂:M₁ instead of M₁:M₂).

⚠️

Student Fallacy (Why candidates pick this trap): Calculating M₂ / M₁ instead of M₁ / M₂.

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NTA Trap Alert: Radius vs. Area Scaling Trap

Students frequently forget that area is proportional to r², selecting 1:2 instead of 1:4.

🛡️ How to avoid the -1 mark: Always remember: Magnetic moment is an AREA property (M = I · A ∝ r²)!

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Core NEET Syllabus Standard

NEET Physics Core Syllabus · Moving Charges and Magnetism Standard Benchmark

Core Scientific Principle Tested:

"Magnetic dipole moment of a circular current loop is M = I π r²."

Syllabus Focus: Circular Current Loop as a Magnetic Dipole

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

Moment means Area: Area scales as r² ⟹ (1/2)² = 1:4!

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NEET 2025 Physics Question 12 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Area Scaling M ∝ r² Rule

Step-by-Step Rigorous Workflow & Mathematical Proof

Formula for Magnetic Dipole Moment

Ratio Calculation

360° Option Elimination Engine Key Feature

NTA Trap Alert: Radius vs. Area Scaling Trap

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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