Question

A particle of charge $q$ and mass $m$ is projected with a velocity $V_{0}$ towards a circular region having uniform magnetic field $B$ perpendicular and into the plane of paper from point $P$ as shown in the figure. $R$ is the radius and $O$ is the centre of the circular region. If the line $OP$ makes angle $\theta $ with the direction of $V_{0}$ , then the value of $V_{0}$ so that particle passes through $O$ is

• A. $\frac{q B R}{m sin \theta }$
• B. $\frac{q B R}{2 m sin \theta }$
• C. $\frac{2 q B R}{m sin \theta }$
• D. $\frac{3 q B R}{2 m sin \theta }$

Answer 1

Answer: (B)

$r=\frac{m V_{0}}{q B}$
$R=2r \, sin\theta $
$\Rightarrow R=\frac{2 m V_{0}}{q B}sin\theta $
$\Rightarrow V_{0}=\frac{q B R}{2 m sin \theta }$