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PhysicsNEET 2025Torque on a current loop, moving-coil galvanometer

Moving Charges and Magnetism

A model for the quantised 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 the 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):

  1. A.heπm\dfrac{he}{\pi m}
  2. B.he2πm\dfrac{he}{2\pi m}✓
  3. C.heBπm\dfrac{heB}{\pi m}
  4. D.heB2πm\dfrac{heB}{2\pi m}

Solution

Flux quantisation: Bπr2=heB\pi r^2 = \frac{h}{e} for the lowest state. In the field, mv=eBrmv = eBr. Magnetic moment μ=evr2=e2Br22m=e2B2m⋅heπB=he2πm\mu = \frac{evr}{2} = \frac{e^2Br^2}{2m} = \frac{e^2B}{2m}\cdot\frac{h}{e\pi B} = \frac{he}{2\pi m}.

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