A bar magnet of original length ℓ and magnetic moment M is bent into an arc subtending 60° at the centre, as shown. What is the new magnetic dipole moment? [Image]
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A bar magnet of original length ℓ and magnetic moment M is bent into an arc subtending 60° at the centre, as shown. What is the new magnetic dipole moment? [Image]

G1 Physics · Accepted Answer

Step 1: Magnetic moment of a straight bar is M=mℓ, where m is pole strength and ℓ is pole separation. Step 2: When bent into a circular arc subtending θ=60°=π/3, arc length remains ℓ=rθ, while the new end-to-end pole separation is chord d=2r sin(θ/2)=r. Step 3: Thus M′=md=M(d/ℓ)=M/θ=3M/π. Answer B, correcting the previous source-import letter A. Final answer: (B) 3M/π.