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Current Loop as a Magnetic Dipole question from NEET 2025

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Current Loop as a Magnetic Dipole

A model for quantized motion of an electron in a uniform magnetic field BB states that the flux passing through the orbit of the electron is n(h/e)n(h/e) where nn is an integer, hh is Planck's constant and ee is the magnitude of electron's charge. According to the model, the magnetic moment of an electron in its lowest energy state will be ( mm is the mass of the electron)

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Answer: (d)

  1. Lowest state n=1n = 1: Bπr2=heB\pi r^2 = \frac{h}{e}, so r2=hπeBr^2 = \frac{h}{\pi eB}.
  2. Circular motion: r=mveB⇒v=eBrmr = \frac{mv}{eB} \Rightarrow v = \frac{eBr}{m}.
  3. μ=ev2πr⋅πr2=evr2=e2Br22m\mu = \frac{ev}{2\pi r}\cdot\pi r^2 = \frac{evr}{2} = \frac{e^2Br^2}{2m}
  4. μ=e2B2m⋅hπeB=he2πm\mu = \frac{e^2B}{2m}\cdot\frac{h}{\pi eB} = \frac{he}{2\pi m}
  5. So the answer is (d).
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