I was trying to compute what is the maximum energy reached by the LHC assuming it has a circunference of 27 km length and the magnetic field of the magnets is ~8 T. To do that, I tried comparing the centripetal force suffered by protons $mv^2/R$ where $m$ is the mass of the proton, $v$ the speed of the particle and $R$ the radius of the circunference with the electromagnetic force $qvB$, with $q$ the charge of a proton and $B$ the magnetic field strength. If I do this, I'm getting a speed larger than the speed of light, so I guess I'm screwing up in some reasoning...
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The proton is relativistic so the centrifugal force term is different. The correct relativistic relation is amazingly simple: $p=0.3 BR$. (Units GeV/c, Tesla, meters).
Your estimate will be a bit high as the ring is not fully occupied by magnets. There are gaps for RF, collimators, quadrupoles, and other components.
RogerJBarlow
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