A deuteron and an alpha particle having equal kinetic energy enter perpendicularly into a magnetic field. Let $r_{d}$ and $r_{\alpha}$ be their respective radii of circular path. The value of $\frac{r_{d}}{r_{\alpha}}$ is equal to:

JEE Main · 2021 · 20 Jul 2021 · Shift 1 · Magnetic Effects of Current

A deuteron and an alpha particle having equal kinetic energy enter perpendicularly into a magnetic field. Let

r_{d}

and

r_{α}

be their respective radii of circular path. The value of

\frac{r _{d}}{r _{α}}

is equal to:

(A) $2$ ✓ Correct
(B)2
(C) $\frac{1}{2}$
(D)1

Answer: (A)

Solution

A charge entering perpendicular to the field moves on a circle of radius

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

. At equal kinetic energy and equal field,

r \propto \frac{m}{q}

. A deuteron has

m = 2 u

and

q = e

, an alpha particle

m = 4 u

and

q = 2 e

, so

\frac{r _{d}}{r _{α}} = \frac{2 u}{e} \times \frac{2 e}{4 u} = 2

The ratio of the radii is

2

JEE Main · 2021 · 20 Jul 2021 · Shift 1 · Single correct option

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