An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii re, rp, rα respectively in a uniform magnetic field B. The relation between re, rp, rα is

Engineering

Physics

Motion of Charged Particle in Uniform Magnetic Field

Question

An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii r_e, r_p, r_α respectively in a uniform magnetic field B. The relation between r_e, r_p, r_α is

r_e < r_p < r_α

r_e > r_p = r_α

r_e < r_α < r_p

r_e < r_p = r_α

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R = $\frac{mv}{qB}$ ......(1)

$\frac{{(P_{e})}^{2}}{2 m_{e}} = \frac{{(P_{P})}^{2}}{2 m_{p}} = \frac{{(P_{α})}^{2}}{2 m_{α}}$ = constant

P_e = $\sqrt{2 m_{e} const .}$

P_p = $\sqrt{2 m_{p} const .}$

P_α = $\sqrt{2 m_{α} const .}$

R = $\frac{\sqrt{2 m const .}}{qB}$

R $\propto \frac{\sqrt{m}}{q}$ r_e < r_p = r_α