Question

A proton and an $\alpha $ -particle are projected normally with the same speed into a magnetic field. What will be the ratio of radii of the trajectories of the proton and $\alpha $ -particle?

• A. $2:1$
• B. $1:2$
• C. $4:1$
• D. $1:4$

Answer 1

Answer: (B)

In perpendicular magnetic field
Magnetic force = centripetal force
$ \, \, \, qvB=\frac{m v^{2}}{r} \, \Rightarrow r=\frac{m v}{q B}$
For proton $ \, q_{1}=e, \, m_{1}=m$
For $\alpha $ -particle $q_{2}=2e, \, m_{2}=4m$
$\therefore \, \, \, \frac{r_{1}}{r_{2}}=\frac{m_{1} v}{q_{1} B} \, \times \frac{q_{2} B}{m_{2} v}$
$ \, \frac{r_{1}}{r_{2}}=\frac{m}{e} \, \times \frac{2 e}{4 m}$
$ \, \frac{r_{1}}{r_{2}}=\frac{1}{2}$