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On Measuring the Mass of a Charged Particle by the Radius of Curvature of its Path in a Magnetic Field |
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Let B be the vertical component of a magnetic field and v be the horizontal velocity of a particle of charge q. The force F on the particle due its traversing the magneic field is given by
It is directed perpendicular to the velocity vector causing the particle to follow a circular path of radius R. If the mass of the particle is m then its centripetal force needed to maintain that path is mv²/R. That means that
Thus the mass of a charged particle is readily measured.
Let φ be the number of times per second that the particle executes its circular orbit; i.e.,
But from the above it is seen that
Thus
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