Search any question & find its solution
Question:
Answered & Verified by Expert
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 radii of circular paths along which the two particles move is :
Options:
Solution:
2253 Upvotes
Verified Answer
The correct answer is:
$4: 3$
$m_1: m_2=1: 1$
$q_1: q_2=1: 2$
$v_1: v_2=2: 3$
Radius of path of chaged particle moving in uniform magnetic field,
$r=\frac{m v}{B q}$
$\therefore \quad \frac{r_1}{r_2}=\left(\frac{m_1}{m_2}\right)\left(\frac{v_1}{v_2}\right) \times\left(\frac{q_2}{q_1}\right)$
$=\frac{1}{1} \times \frac{2}{3} \times \frac{2}{1}=\frac{4}{3}$
$r_1: r_2=4: 3$
$q_1: q_2=1: 2$
$v_1: v_2=2: 3$
Radius of path of chaged particle moving in uniform magnetic field,
$r=\frac{m v}{B q}$
$\therefore \quad \frac{r_1}{r_2}=\left(\frac{m_1}{m_2}\right)\left(\frac{v_1}{v_2}\right) \times\left(\frac{q_2}{q_1}\right)$
$=\frac{1}{1} \times \frac{2}{3} \times \frac{2}{1}=\frac{4}{3}$
$r_1: r_2=4: 3$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.