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Particle moving in electromagnetic field - converting units

  • Thread starter bossman27
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Homework Statement


Show that the force on a moving charged particle F = qv × B
from a magnetic field pointing perpendicular to the velocity produces a centripetal force and that this is equivalent to the equation pc = ABρ, where B is the magnetic field strength (in Tesla) and ρ is the radius of the circular orbit (in meters). If we express p in GeV/c, what
is the value of the constant A (which has units GeV/T-m) for a proton?


Homework Equations





The Attempt at a Solution



I had no trouble with the first part of the problem. Since v is perpendicular to B, I just used F=(mv^2)/r and then multiplied both sides by c to get pc = qcB(rho). Now I have A = qc = 1.6x10^-19 C x c, however this is my first time working with eV units and am a bit lost on how to go about converting 'charge*c' to GeV/T-m.
 

Answers and Replies

  • #2
Simon Bridge
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Your first step is to demonstrate circular motion.

After that, do your calculation in GeV from the get-go. note that mc2=0.938GeV

[tex]evB=\frac{mv^2}{r}=\frac{p^2}{mr}=\frac{(pc)^2}{mc^2r}[/tex]

Or do the dimensional analysys on your units (Cm/s) to make sure they come out to Joules/(Tesla-meters) then just convert the Joules to GeV by the usual conversion factor.
 

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