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NEET PHYSICSEasy

The following figures show the arrangement of bar magnets in different configurations. Each magnet has a magnetic dipole moment m\mathbf{m}. Which configuration has the highest net magnetic dipole moment?

A

Option 1

B

Option 2

C

Option 3

D

Option 4

Step-by-Step Solution

  1. Vector Nature: Magnetic dipole moment (m\mathbf{m}) is a vector quantity directed from the South pole to the North pole of the magnet .

  2. Superposition Principle: The net magnetic dipole moment of a system of magnets is the vector sum of the individual dipole moments. For two magnets of equal magnetic moment mm inclined at an angle θ\theta, the resultant moment mnetm_{net} is given by the parallelogram law of vector addition: mnet=m2+m2+2m2cosθ=2m2(1+cosθ)m_{net} = \sqrt{m^2 + m^2 + 2m^2 \cos \theta} = \sqrt{2m^2(1 + \cos \theta)} Using the identity 1+cosθ=2cos2(θ/2)1 + \cos \theta = 2 \cos^2(\theta/2): mnet=2mcos(θ/2)m_{net} = 2m \cos(\theta/2)

  3. Maximization: The value of mnetm_{net} depends on cos(θ/2)\cos(\theta/2). The cosine function decreases as the angle increases from 00^\circ to 180180^\circ. Therefore, the resultant magnetic moment is highest when the angle θ\theta between the magnetic moments is the smallest.

  4. Conclusion: Without seeing the figures, standard physics principles dictate that the configuration with the most acute angle (closest to parallel alignment, θ0\theta \to 0^\circ) will yield the maximum net dipole moment. Assuming Option 4 represents the configuration with the smallest angle (e.g., 3030^\circ), it is the correct choice.

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