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If we want to show whether or not a specific Cosmic Ray particle is confined to our galaxy we must use the Larmor radius (relativistic version),

$$r = \gamma \, \frac{ m c}{q B}$$

Considering a $10^{14}$ eV proton and assuming the galactic magnetic field strength is $10^{-11}$ T, show that the particle is confined to the Milky Way (radius $15$ kpc).

How can we use the Larmor radius to prove that the particle is in fact confined to the Milky Way?

Attempt:

$$r = \frac{p}{qB}, \,\,\,\,\, p=\gamma mc$$ Therefore $$r=\frac{E}{cqB}$$ and substituting values in yields $$r = \frac{10^{14}}{(3\times10^8)(1.6\times10^{-19})(10^{-11})}$$ such that $$r \sim10^{36} \,\,\,\,\text{(meters?)}$$

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  • $\begingroup$ $10^{36}$ meters is pretty far. Are you sure your units work out right? $\endgroup$ – Kyle Kanos Apr 9 at 15:01
  • $\begingroup$ I think if should convert the Energy from eV to Joules, which instead returns a value of $10^{17}$ meters, which is approximately 1 parsec? $\endgroup$ – LightningStrike Apr 9 at 15:04
  • $\begingroup$ And how large is a galaxy compared to a parsec? $\endgroup$ – Anders Sandberg Apr 9 at 15:37
  • $\begingroup$ Actually $E/q=10^{14}$V, the $B\sim \frac{Vs}{m^2}$, then $r$ is in meter after throwing $1.6\cdot 10^{-19}$ out of the right side of the equation. $\endgroup$ – Frederic Thomas Apr 9 at 17:43

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