JEE Main · 2021 · 18 Mar 2021 · Shift 2 · Magnetic Effects of Current

A proton and an

α

-particle, having kinetic energy

K_{p}

and

K_{α}

respectively, enter into a magnetic field at right angles. The ratio of the radii of trajectory of proton to that of

α

-particle is

2 : 1

. The ratio of

K_{p} : K_{α}

Answer: (D)

Solution

A particle of mass

m

and charge

q

entering a field

B

at right angles moves on a circle of radius

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

For the proton

r_{p} = \frac{2 m _{p} K _{p}}{e B}

. The

α

-particle has mass

4 m_{p}

and charge

2 e

, so

r_{α} = \frac{2 ( 4 m _{p} ) K _{α}}{2 e B} = \frac{2 m _{p} K _{α}}{e B}

The mass and charge factors cancel between the two, leaving

\frac{r _{p}}{r _{α}} = \frac{K _{p}}{K _{α}} = 2

, so the kinetic energies are in the ratio

K_{p} : K_{α} = 4 : 1

JEE Main · 2021 · 18 Mar 2021 · Shift 2 · Single correct option