A charged particle `+q` of mass `m` is placed at a distance `d` from another charge particle `-2q` of mass `2m` in a uniform magnetic field of induction vectro `B` as shown in the fig.If the particles are projected towards each other with equal speeds `v`.(Neglect the interaction between the particles)
(a)Find the maximum value of the projection speed `V_(max)` so that the two particles do not collide.
b)Find the time interval after which collision occurs between the particles if projection speed equals `2V_(max)`
(c)In the previous part,assuming that the particles stick after the collision find the radius of the circular path of the particle in subsequent motion.

Answer

(a)`V_(max)=(qBd)/(2m)` (b)`(pid)/(12 V_(max))=(pim)/(6qB)`
(c)`sqrt3d`

Explanation

Final mass `=3m`
Final charge `=-q`
`R_(f)=(3mV)/(qB)`
By conservation of linear momentum
`2 mV_(m)sin pi/6+4mV_(m)sin pi/6=3mV_(y)`
`4 mV_(m)cos pi/6-2mV_(m)cos pi/6=3mV_(x)`
`V_(x)=V_(m)/sqrt3`
`V=sqrt(V_(x)^(2)+V_(y)^(2))=(2Vm)/sqrt3, R_(f)=(6mV_(m))/(qBsqrt3)=(2sqrt3_(m))/(qB)xx(qBd)/(2m)=sqrt3 d`