A particle is moving in a circular trajectory because of a magnetic field. Show that regardless of the veolocity of the particle, it will take the same amount of time to complete one revolution.
I'm not sure how to prove this. Should i use the formula for circle trajectories..qvB=mv^2/r?
Yes, use that formula. The period will be 2 pi r/v, which is proportional to r/v.
Note that qB = mv/r, which means
r/v = m /(q B)
That is independent of v.