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MHT CET 2026 (12 May, Shift 1) · Current Loop as a Magnetic Dipole

Current Loop as a Magnetic Dipole question from MHT CET 2026 (12 May, Shift 1)

Q17MHT CET 2026 · 12 MAY · SHIFT 1Difficult

Current Loop as a Magnetic Dipole

A charge qq is circulating at a constant speed vv with a semicircular loop of radius rr. The magnetic moment of this loop is

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Answer: (c)

  1. Perimeter of the semicircular loop =πr+2r= \pi r + 2r, so T=r(π+2)vT = \frac{r(\pi + 2)}{v} and I=qT=qvr(π+2)I = \frac{q}{T} = \frac{qv}{r(\pi + 2)}.
  2. Area A=πr22A = \frac{\pi r^2}{2}.
  3. m=IA=qvr(π+2)⋅πr22=πrqv2(π+2)m = IA = \frac{qv}{r(\pi+2)}\cdot\frac{\pi r^2}{2} = \frac{\pi rqv}{2(\pi + 2)}
  4. So the answer is (c).
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