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
$qvB=\frac{m{v}^2}{r}\Rightarrow r=\frac{mv}{qB}$
For proton $q_1=e,m_1=m$
For $\alpha$ -particle $q_2=2e,m_2=4m$
$\therefore \frac{r_1}{r_2}=\frac{m_{1}v}{q_{1}B}\times \frac{q_{2}B}{m_{2}v}$
$\frac{r_1}{r_2}=\frac{m}{e}\times \frac{2e}{4m}$
$\frac{r_1}{r_2}=\frac{1}{2}$