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JEE Main 2022 (27 Jun, Shift 2) · Moving Charge in a Magnetic Field

Moving Charge in a Magnetic Field question from JEE Main 2022 (27 Jun, Shift 2)

Q54JEE Main 2022 · 27 JUN · SHIFT 2Easy

Moving Charge in a Magnetic Field

A deuteron and a proton moving with equal kinetic energy enter into a uniform magnetic field at right angle to the field. If rd and rp are the radii of their circular paths respectively, then the ratio $\frac{r_d}{r_p}$ will be $\sqrt{x}$ : 1 where x is __________.

Numerical answer type. Work it out, then open the answer.

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Answer: 2

$r = \dfrac{\sqrt{2mK}}{qB}$ ; same $K$ , same charge $e$ , same $B$ $\Rightarrow r \propto \sqrt{m}$
$m_d = 2m_p \Rightarrow \dfrac{r_d}{r_p} = \sqrt{2}$
So $x = 2$ .

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