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. What is the relation between re, rp, r_α?

PhysicsMediumHigh School (11–12)jee-main

For a charged particle moving in a circle in a magnetic field, the radius is $r = \dfrac{mv}{qB} = \dfrac{\sqrt{2mK}}{qB}$ , where $K$ is the kinetic energy. So for fixed $K$ and $B$ , $r \propto \dfrac{\sqrt{m}}{q}$ .

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 $B$ . What is the relation between $r_e$ , $r_p$ , $r_\alpha$ ?

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