An `alpha`-particle and a proton are moving in the plane of the paper in a region where there is a uniform magnetic field `vecB` directed normal to the plane of the paper. If the two particles have equal linear momenta, what will be the ratio of their trajectories in the field?

Explanation

When a charged particle of charge q moving with velocity v is subjected to normal magnetic field B, then it describe a circular path of radius r given by
`Bqv=(mv^2)/(r)` or `r=(mv)/(Bq)=(p)/(Bq)`
where p=momentum of the particle
For the same values of p and B, `rprop1//q`
`:. r_alpha/r_p=q_p/q_alpha=(e)/(2e)=1/2`