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NEET PHYSICSMAGNETISM AND MATTEREasy

Question

The length of a magnetized iron bar is LL and its magnetic moment is MM. When this bar is bent to form a semicircle its magnetic moment is:

A

MM

B

Mπ2\frac{M\pi}{2}

C

M2π\frac{M}{2\pi}

D

2Mπ\frac{2M}{\pi}

Step-by-Step Solution

  1. Initial State: The magnetic moment MM of a straight bar magnet is defined as the product of its pole strength (mm) and the separation distance between the poles (LL). M=m×LM = m \times L
  2. Bending Geometry: When the bar is bent into a semicircle, the length of the arc remains LL. Let the radius of the semicircle be rr. From the geometry of a circle: Arc Length=πr=L  ⟹  r=Lπ\text{Arc Length} = \pi r = L \implies r = \frac{L}{\pi}
  3. New Effective Length: The new magnetic moment (M′M') depends on the vector displacement (shortest straight-line distance) between the two poles. For a semicircle, this distance is the diameter (2r2r). Reference to displacement vectors can be found in kinematics . L′=2r=2LπL' = 2r = \frac{2L}{\pi}
  4. Calculation: M′=m×L′=m×(2Lπ)=2π(mL)M' = m \times L' = m \times \left(\frac{2L}{\pi}\right) = \frac{2}{\pi} (m L) Substituting M=mLM = mL: M′=2MπM' = \frac{2M}{\pi}

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from MAGNETISM AND MATTER. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSMAGNETISM AND MATTERlengthmagnetizedmagneticmomentsemicircle

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