
72 Classical Mechanics
© 2010 Taylor & Francis Group, LLC
We see that
= constant
; the particle, therefore, moves with a uniform velocity along the direction
of
. Also,
is always perpendicular to both
⊥
and
, so the perpendicular component makes
the particle travel in a circular path (Figure 3.7).
To nd the radius R of the circle, we recognize that the Lorentz force qv
⊥
B provides the particle
with the centripetal force
⊥
2
/ that keeps it moving in a circle. Equating the Lorentz and centrip-
etal forces, we have
Bm
=
2
/ .
Solving for R,
R
mv
qB
=
⊥
. (3.42)
The radius R is often called the Larmor radius of the particle. We can ...