An electron, a proton, and an alpha particle, all having the same kinetic energy, move in circular orbits of radii re, rp, r_α respectively in a uniform magnetic field B. Which relation holds among the radii?

PhysicsMediumHigh School (11–12)jee-main

For a charged particle moving in a magnetic field, the radius of its circular path is $r = \dfrac{\sqrt{2mK}}{qB}$ , where $K$ is the kinetic energy, $m$ the mass, and $q$ the charge. Comparing particles of different mass-to-charge ratios at the same $K$ reveals which traces the largest or smallest circle.

An electron, a proton, and an alpha particle, all having the same kinetic energy, move in circular orbits of radii $r_e$ , $r_p$ , $r_\alpha$ respectively in a uniform magnetic field $B$ . Which relation holds among the radii?

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