Two particle, each having a mass `m` are placed at a separation `d` in a uniform magnetic field `B` as shown in figure.They have opposite charges of equal magnitude `q`.At time `t=0`, the particles are projected towards each other, each with a speed `v`.
At what instant will a collision occur between the particles if `v=2v_(m)`?

Explanation

`d=2R_(m)`
`d=2(mV_(m))/(qB)`
`V_(m)=(qBd)/(2m)`

`R=(m(V_(m))/(4))/(qB)=(R_(m))/(4)`
min distance `=d-(d)/(4)=(3d)/(4)`

max distance `=d+(d)/(4)=(5d)/(4)`

`4R_(m)sin theta=d`
`2d sintheta=d`
`sin theta=(1)/(2),theta=(pi)/(6)`
`omega=(qB)/(m)`
`t=(pi//6)/(omega)=(pim)/(6qB)`