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

JEE Main · 2018 · 08 Apr 2018 · Offline · Magnetic Effects of Current

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:

Answer: (C)

In a magnetic field the orbit radius for a particle of given kinetic energy is

r = \frac{2 K m}{q B}

, so for equal

K

and

B

it scales as

\frac{m}{q}

. For the electron this is

\frac{m _{e}}{e}

, for the proton

\frac{m _{p}}{e}

, and for the alpha particle

\frac{4 m _{p}}{2 e} = \frac{m _{p}}{e}

, the same as the proton. Since the electron is far lighter its radius is much smaller, giving

r_{e} < r_{p} = r_{α}

JEE Main · 2018 · 08 Apr 2018 · Offline · Single correct option