Question

Two particles of charges $+Q$ and $-Q$ are projected from the same point with a velocity $v$ in a region of uniform magnetic field $B$ such that the velocity vector makes an angle $q$ with the magnetic field. Their masses are $M$ and $2M$, respectively. Then, they will meet again for the first time at a point whose distance from the point of projection is

• A. $\frac{2\pi Mv\cos \theta }{QB}$
• B. $\frac{8\pi Mv\cos \theta }{QB}$
• C. $\frac{\pi Mv\cos \theta }{QB}$
• D. $\frac{4\pi Mv\cos \theta }{QB}$

Answer 1

The correct option is D $\frac{4\pi Mv\cos \theta }{QB}$

Both particles will move in helix. They will meet for the first time when mass m will complete two revolutions and mass 2m will complete one revolution. Time taken to complete one rotation.

$t_1=2\ast \left(\frac{2\pi M}{qB}\right)=\frac{4\pi M}{qB}$

$t_2=\left(\frac{2\pi \left(2M\right)}{qB}\right)=\frac{4\pi M}{qB}$

Hence distance from the projection

$=t\ast \left(\vartheta cos\theta \right)$

$=\frac{4\pi M}{qB}\ast \vartheta cos\theta$

$=\frac{4\pi M\vartheta cos\theta }{qB}$