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,
$r=\frac{m v}{B q}$
$∴ \, \, \, \frac{r_{1}}{r_{2}}=\left(\frac{m_{1}}{m_{2}}\right) \, \left(\frac{v_{1}}{v_{2}}\right) \, \times \left(\frac{q_{2}}{q_{1}}\right)=\frac{1}{1}\times \frac{2}{3}\times \frac{2}{1}=\frac{4}{3}$
$r_{1}:r_{2}=4:3$