Question

Two particles $X$ and $Y$ having equal charges, are accelerated through the same potential difference. They enter a region of a uniform magnetic field and describe a circular path of radii $r_1$ and $r_2$ respectively. The ratio of the mass of $X$ to that of $Y$ is

• A. $\frac{r_1}{r_2}$
• B. $\sqrt{\frac{r_1}{r_2}}$
• C. ${\left[\frac{r_2}{r_1}\right]}^2$
• D. ${\left[\frac{r_1}{r_2}\right]}^2$

Answer 1

Answer: (D)

The force acting on the particle inside the magnetic field is $F_B=qvBsin\theta$
$\theta =90^{\circ }$ , $F_B=qvB$
This provides the necessary centripetal force $F_c=\frac{m{v}^2}{r}$
$\therefore \frac{m{v}^2}{r}=qvB\Rightarrow r=\frac{mv}{qB}$ $=\sqrt{\frac{2mqV}{qB}}$
$\frac{r_1}{r_2}=\sqrt{\frac{m_x}{m_y}}$
$\frac{m_x}{m_y}={\left(\frac{r_1}{r_2}\right)}^2$