Question

A charged particle $+q$ of mass $m$ is placed at a distance $d$ from another charged particle $-2q$ of mass $2m$ in a uniform magnetic field of induction vector $B$ with direction into the plane of paper (as shown in figure). If particles are projected towards each other with equal speeds $V_0$, the maximum value of the projection speed $V_0$, so that the two particles do not collide is :
(Assume only magnetic force of interaction between particles)

• A. $\frac{qBd}{m}$
• B. $\frac{qBd}{2m}$
• C. $\frac{2qBd}{m}$
• D. $\frac{3qBd}{m}$

Answer 1

Answer: (B)

$\frac{qBd}{2m}$

Particle can go upto a distance of circle made by it
due to magnetic field
$d=r_1+r_2$
$d=\frac{m{V}_0}{qB}+\frac{2m{V}_0}{2qB}$
$d=\frac{2m{V}_0}{qB}$
$V_0=\frac{qBd}{2m}$