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The radius of the circular path of a particle of mass \( m \) and charge \( Q \) moving at speed \( v \) perpendicular to a field \( B \) is

  • A.\( QB/(mv) \)
  • B.\( mv^2/(QB) \)
  • C.\( mvB/Q \)
  • D.\( mv/(QB) \)

Answer: D

Equating the magnetic force to the centripetal force gives this result at once. It is the basis of the mass spectrometer, since particles of the same charge and speed separate by mass, and of the cyclotron, whose period turns out to be independent of the speed.

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