Q.46 Physics ⭐ 360° Option Elimination Active

NEET 2021 Physics Question 46 Solution

Topic: Moving Charges and Magnetism · Official NTA Booklet Code M1

Question

A uniform conducting wire of length 12a and resistance 'R' is wound up as a current carrying coil in the shape of, (i) an equilateral triangle of side 'a'. (ii) a square of side 'a'. The magnetic dipole moments of the coil in each case respectively are:

✓

Verified Against NTA Final Answer Key

Option (1) : √3 I a^2 and 3 I a^2

📚 Moving Charges and Magnetism Medium

📋 Given Parameters & Problem Setup

Total Length of Wire (L) 12 a

Current in Wire I

Coil (i) Shape Equilateral triangle of side a

Coil (ii) Shape Square of side a

⚡

The 30-Second Exam Hall Shortcut: ⚡ Turns × Area: N = L / Perimeter

⏱️ Save ~25 seconds

Triangle: Perimeter $= 3a \implies N_1 = \frac{12a}{3a} = 4$ turns. Area $= \frac{\sqrt{3}}{4}a^2$ . $M_1 = N_1 I A_1 = 4 \times I \times \frac{\sqrt{3}}{4}a^2 = \sqrt{3} I a^2$ . Square: Perimeter $= 4a \implies N_2 = \frac{12a}{4a} = 3$ turns. Area $= a^2$ . $M_2 = N_2 I A_2 = 3 \times I \times a^2 = 3 I a^2$ . Match Option (1)!

1 Total wire length is

L = 12a

2 Case (i) Equilateral triangle: perimeter per turn

= 3a

. Number of turns

N_1 = 12a / 3a = 4

3 Area of triangle

A_1 = \frac{\sqrt{3}}{4} a^2

4 Magnetic moment

M_1 = N_1 I A_1 = 4 \cdot I \cdot \left(\frac{\sqrt{3}}{4} a^2\right) = \sqrt{3} I a^2

5 Case (ii) Square: perimeter per turn

= 4a

. Number of turns

N_2 = 12a / 4a = 3

6 Area of square

A_2 = a^2

7 Magnetic moment

M_2 = N_2 I A_2 = 3 \cdot I \cdot a^2 = 3 I a^2

8 Respectively:

\sqrt{3} I a^2

and

3 I a^2

. Match Option (1).

🛡️

Why You Can 100% Trust This Shortcut: Canonical definition of magnetic dipole moment of planar current loop (

M = N I A

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Formula for Magnetic Dipole Moment of a Planar Coil

For a flat coil with $N$ turns, carrying current $I$ and enclosing cross-sectional area $A$ , the magnitude of the magnetic dipole moment is:

M = N I A

Step 2

Analyzing Case (i): Equilateral Triangle of Side a

The perimeter of one triangular loop of side $a$ is $P_1 = 3a$ . With total length $L = 12a$ : - Number of turns: $N_1 = \frac{L}{3a} = \frac{12a}{3a} = 4$ - Area of one equilateral triangle: $A_1 = \frac{\sqrt{3}}{4} a^2$

M_1 = N_1 I A_1 = 4 \times I \times \left(\frac{\sqrt{3}}{4} a^2\right) = \sqrt{3} I a^2

Step 3

Analyzing Case (ii): Square of Side a

The perimeter of one square loop of side $a$ is $P_2 = 4a$ . With total length $L = 12a$ : - Number of turns: $N_2 = \frac{L}{4a} = \frac{12a}{4a} = 3$ - Area of one square: $A_2 = a^2$

M_2 = N_2 I A_2 = 3 \times I \times (a^2) = 3 I a^2

⭐

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:

Exact magnetic moments: $M_1 = 4 \times I \times (\sqrt{3}/4 a^2) = \sqrt{3}Ia^2$ and $M_2 = 3 \times I \times a^2 = 3Ia^2$ .

💡

Why this is airtight: None; rigorous geometry and magnetic moment analysis.

2 2

✗ Incorrect

Verdict & Scientific Reason:

Incorrect turn calculation for both coils.

⚠️

Student Fallacy (Why candidates pick this trap): Assuming single-turn coils with incorrect area.

3 3

✗ Incorrect

Verdict & Scientific Reason:

Swaps the number of turns and ignores $\sqrt{3}/4$ factor for triangle.

⚠️

Student Fallacy (Why candidates pick this trap): Using square area for triangle.

4 4

✗ Incorrect

Verdict & Scientific Reason:

Ignores the $\frac{\sqrt{3}}{4}$ area factor of the equilateral triangle ( $4 \times I a^2$ ).

⚠️

Student Fallacy (Why candidates pick this trap): Forgetting to multiply by

\frac{\sqrt{3}}{4}

for equilateral triangle.

⚠️

NTA Trap Alert: Number of Turns Neglect Trap

Students frequently assume the coil has only 1 turn ( $N = 1$ ), calculating $M_1 = \frac{\sqrt{3}}{4}Ia^2$ and $M_2 = Ia^2$ . Total wire length is $12a$ , creating multiple full loops ( $N_1 = 4, N_2 = 3$ ).

🛡️ How to avoid the -1 mark: Always check total wire length:

N = \text{Total Length} / \text{Perimeter}

📖

Core NEET Syllabus Standard

NCERT Physics · Moving Charges and Magnetism Standard Benchmark

Core Scientific Principle Tested:

"The magnetic dipole moment of a coil of $N$ turns and area $A$ is $M = NIA$ ."

Syllabus Focus: Magnetic Dipole Moment of a Current Loop

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

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NEET 2021 Physics Question 46 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Turns × Area: N = L / Perimeter

Step-by-Step Rigorous Workflow & Mathematical Proof

Formula for Magnetic Dipole Moment of a Planar Coil

Analyzing Case (i): Equilateral Triangle of Side a

Analyzing Case (ii): Square of Side a

360° Option Elimination Engine Key Feature

NTA Trap Alert: Number of Turns Neglect Trap

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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