Question

The velocity of two $\alpha$ particles A and B, in a uniform magnetic field is in the ratio of $1:3$. They move in different circular orbits in the magnetic field. The ratio of radius of curvatures of their paths is:

• A. $1:2$
• B. $1:3$
• C. $3:1$
• D. $2:1$

Answer 1

Answer: (B)

$1:3$

Given : $\frac{v_A}{v_B}=\frac{1}{3}$

Using $mv=Bqr$

$⟹$ $r=\frac{mv}{Bq}$

As both are $\alpha$ particles, thus both have same mass and charge respectively.

$\therefore$ $r\propto v$ (And $B$ is also same for both)

$⟹$ $\frac{r_A}{r_B}=\frac{v_A}{v_B}=\frac{1}{3}$