San José State University
Thayer Watkins
Silicon Valley
& Tornado Alley

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


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

R/v = m/(qB)
and hence
φ = 2πm/(qB)


m = φqB/(2π)

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