Question

A particle of charge $q$ and mass $m$ is moving with a velocity $- v \hat{i} ( v \neq 0)$ towards a large screen placed in the $Y-Z$ plane at a distance $d$. If there is a magnetic field $\vec{ B }= B _{0} \hat{ k },$ the minimum value of $v$ for which the particle will not hit the screen is:

• A. $\frac{ qdB _{0}}{2 m }$
• B. $\frac{ qdB _{0}}{ m }$
• C. $\frac{2 qdB _{0}}{ m }$
• D. $\frac{ qdB _{0}}{3 m }$

Answer 1

Answer: (B)

In uniform magnetic field particle moves in a circular path, if the radius of the circular path is $'d'$, particle will not hit the screen.
$d =\frac{ mv }{ qB _{0}}$
$v =\frac{ qB _{0} d }{ m }$