Savchenko Problem 14.4.20

The key insight is that a charged particle moving perpendicular to a magnetic field follows a circular path whose radius depends on the particle's momentum, not its energy alone. You'll need to convert the given energy to momentum using the relativistic energy-momentum relation $E^2 = (pc)^2 + (m_0c^2)^2$, then apply the radius formula $r = \frac{p}{qB}$. Since protons and electrons have the same charge magnitude but vastly different rest masses, at the same energy the electron will be ultra-relativistic while the proton may not be—leading to very different required radii.

The key insight is that a charged particle moving perpendicular to a magnetic field follows a circular path whose radius depends on the particle's momentum, not its energy alone. You'll need to convert the given energy to momentum using the relativistic energy-momentum relation $E^2 = (pc)^2 + (m_0c^2)^2$, then apply the radius formula $r = \frac{p}{qB}$. Since protons and electrons have the same charge magnitude but vastly different rest masses, at the same energy the electron will be ultra-relativistic while the proton may not be—leading to very different required radii.