﻿ On Measuring the Mass of a Charged Particle by the Radius of Curvature of its Path in a Magnetic Field
San José State University

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Thayer Watkins
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On Measuring the Mass
of a Charged Particle
of its Path in a Magnetic Field

## Analysis

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

#### F = qvB

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

#### mv²/R = F = qvB and therefore mv/R = qB and furthermore m = qBR/v

Thus the mass of a charged particle is readily measured.

## Mass in terms of Frquency

Let φ be the number of times per second that the particle executes its circular orbit; i.e.,

#### φ = 2πR/v

But from the above it is seen that

Thus