Question

Two particles having the same momentum enter at right angles into same magnetic field and travel in circular paths of radius $r_1$ and $r_2$. The ratio of their charges is:

• A. $\frac{r_1}{r_2}$
• B. $(\frac{r_1}{r_2}{)}^{1/2}$
• C. $(\frac{r_1}{r_2}{)}^2$
• D. $(\frac{r_1}{r_2}{)}^{-1}$

Answer 1

The correct option is D $(\frac{r_1}{r_2}{)}^{-1}$

Since the momentum is same,

$m_1{v}_1=m_2{v}_2=p$
Centripetal force is equal to the magnetic force applied.

Hence, $\frac{m{v}^2}{r}=qvB$

Therefore, Radius of curvature is given by:

$r=\frac{mv}{qB}=\frac{p}{qB}$

$r_1=\frac{p}{q_{1}B}$
$r_2=\frac{p}{q_{2}B}$
$\frac{q_1}{q_2}=\frac{r_2}{r_1}$