Question

Two ions having masses in the ratio $1:1$ and charges $1:2$ are projected into uniform magnetic field perpendicular to the field with speeds in the ratio $2:3$ . The ratio of the radius of circular paths along which the two particles move is

• A. $4:3$
• B. $2:3$
• C. $3:1$
• D. $1:4$

Answer 1

Answer: (A)

$m_1:m_2=1:1$
$q_1:q_2=1:2$
$v_1:v_2=2:3$
Radius of path of charged particle moving in uniform magnetic field,
$r=\frac{mv}{Bq}$
$\therefore \frac{r_1}{r_2}=\left(\frac{m_1}{m_2}\right)\left(\frac{v_1}{v_2}\right)\times \left(\frac{q_2}{q_1}\right)=\frac{1}{1}\times \frac{2}{3}\times \frac{2}{1}=\frac{4}{3}$
$r_1:r_2=4:3$