Q128 / 180 · KCET 2007 · Physics

A proton and a deuteron with the same initial kinetic energy enter a magnetic field in a direction perpendicular to the direction of the field. The ratio of the radii of the circular trajectories described by them is

  • A
    $1: 4$
  • Correct answer
    B
    $1: \sqrt{2}$
  • C
    $1: 1$
  • D
    $1: 2$

Solution

For a moving charge in a perpendicular magnetic field $$ \frac{m v^{2}}{r}=B q v \Rightarrow r=\frac{m v}{B q}=\frac{p}{B q} $$ $$ \frac{r_{p}}{r_{d}}=\frac{p_{p}}{p_{d}} $$ or or Also, momentum $p=\sqrt{2 m E}$ (as $q$ is same for both) $\frac{p_{p}}{p_{d}}=\sqrt{\frac{m_{p}}{m_{d}}}$ From Eq. (i) and (ii), we have $$ \frac{r_{p}}{r_{d}}=\sqrt{\frac{m_{p}}{m_{d}}}=\sqrt{\frac{1}{2}}=\frac{1}{\sqrt{2}} $$

Hence, the correct answer is option: 'B'.

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