Q.50 Physics · Section B ⭐ 360° Option Elimination Active

NEET 2024 Physics Question 50 Solution

Topic: Magnetism and Matter · Official NTA Booklet Code T1

Question

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Verified Against NTA Final Answer Key

Option (4) : M / 2

📚 Magnetism and Matter Easy

📋 Given Parameters & Problem Setup

Initial bar magnet Length L, magnetic dipole moment M

Pole strength m (unchanged upon bending)

Bending location Bent at the exact midpoint (each arm has length L / 2)

Angle between arms 60°

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The 30-Second Exam Hall Shortcut: ⚡ Equilateral Triangle Vector Shortcut

⏱️ Save ~40 seconds

Two arms of length L/2 at 60° form an EQUILATERAL triangle -> Distance between the two poles is simply L/2 -> M’ = m × (L/2) = M / 2!

1 Original dipole moment: M = m × L, where m is the magnetic pole strength.

2 The bar is bent in the middle into two arms, each of length L/2, with an angle of 60° between them.

3 An isosceles triangle with an included angle of 60° is an EQUILATERAL triangle!

4 Therefore, the straight-line distance between the two poles (effective length L’) is identically L/2.

5 New magnetic moment: M’ = m × L’ = m × (L/2) = M / 2.

6 Option (4) in under 5 seconds!

🛡️

Why You Can 100% Trust This Shortcut: Magnetic Dipole Moment Vector Definition (M = m · L_effective, where L_effective is the straight-line displacement between poles).

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Definition of Initial Magnetic Dipole Moment

For a straight iron bar magnet of length L with pole strengths -m (South pole) and +m (North pole), the magnetic dipole moment is defined as the product of pole strength and magnetic length:

M = m \cdot L

Step 2

Geometry After Bending at Midpoint

When the bar is bent at its midpoint, it forms two straight segments of equal length l_1 = l_2 = L/2 meeting at an angle θ = 60°. Bending the magnet does not alter the intrinsic pole strength m at the ends.

l_1 = l_2 = \frac{L}{2}, \quad \theta = 60^\circ

Step 3

Determination of Effective Separation L’

The effective magnetic dipole moment depends on the direct straight-line distance L’ between the South pole and the North pole at the ends of the bent arms. Applying the law of cosines or isosceles geometry:

L' = 2 \left(\frac{L}{2}\right) \sin\left(\frac{\theta}{2}\right) = L \sin(30^\circ) = L \left(\frac{1}{2}\right) = \frac{L}{2}

Step 4

Calculation of New Magnetic Moment M’

The new magnetic dipole moment M’ is the product of pole strength m and effective separation L’:

M' = m \cdot L' = m \cdot \left(\frac{L}{2}\right) = \frac{m L}{2} = \frac{M}{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)

✗ Incorrect

Verdict & Scientific Reason:

Bending can never increase the effective distance between poles.

⚠️

Student Fallacy (Why candidates pick this trap): Multiplying by 2 instead of dividing.

2 (2)

✗ Incorrect

Verdict & Scientific Reason:

Incorrect trigonometric factor.

⚠️

Student Fallacy (Why candidates pick this trap): Using tan(30°) or cot(60°).

3 (3)

✗ Incorrect

Verdict & Scientific Reason:

Ignores the geometrical reduction in distance between the poles.

⚠️

Student Fallacy (Why candidates pick this trap): Assuming magnetic moment is a scalar conserved quantity like mass.

4 (4)

✓ 100% Correct

Verdict & Scientific Reason:

Exact equilateral triangle result: L’ = L/2 -> M’ = M/2.

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Why this is airtight: None.

⚠️

NTA Trap Alert: Treating Magnetic Moment as a Conserved Scalar

Students often believe that because no mass is lost, the magnetic moment remains M (Option 3).

🛡️ How to avoid the -1 mark: Magnetic moment is a VECTOR pointing from S to N. Bending brings the poles closer together, strictly decreasing the effective vector length!

📖

Core NEET Syllabus Standard

Physics Core Magnetism · Magnetism and Matter Standard Benchmark

Core Scientific Principle Tested:

"The magnetic moment of a bent bar magnet is M’ = 2(M/2) sin(θ/2) = M sin(θ/2)."

Syllabus Focus: The Magnetic Dipole and Dipole Moment

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

60 degrees gives equilateral side: Effective length is halved in stride (M / 2)!

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NEET 2024 Physics Question 50 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Equilateral Triangle Vector Shortcut

Step-by-Step Rigorous Workflow & Mathematical Proof

Definition of Initial Magnetic Dipole Moment

Geometry After Bending at Midpoint

Determination of Effective Separation L’

Calculation of New Magnetic Moment M’

360° Option Elimination Engine Key Feature

NTA Trap Alert: Treating Magnetic Moment as a Conserved Scalar

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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