PHY6040  Nuclear and Particle Detectors  Dr C N Booth 
Since  and 
centripetal acceleration is  
then 
If the particle's velocity makes an angle θ to the direction of the magnetic field, then the trajectory is a helix, with radius
Frequently with high momentum particles, only an arc corresponding
to a small part of the circle is observed. Consider a particle of
momentum p passing through a region, of length L, with a
magnetic field B. The deviation from a straight line, s,
is known as the sagitta of the track (from the Latin word for a
bow).
This can be calculated as follows: 
We previously showed that  
or 

It is also important to consider the error on any measurement of momentum. This is related to the error on the measured sagitta, δs, as follows.
The important result here is that the fractional error on the momentum is proportional to the momentum of the particle.
For a more detailed discussion of the trajectory of a charged particle in a magnetic fiels, see the entry in the BriefBook.