Question

define cyclotron and derive their formula

Answer 1

here friend's your answer is as follows:

cyclotron is an apparatus in which charged atomic and subatomic particles are accelerated by an alternating electric field while following an outward spiral or circular path in a magnetic field.

and here's its formula friend's,
the cyclotron formula gives the radius r of a particle's orbit in a cyclotron and can be derived as followed:
F centripetal = F magnetic

I hope it provides you a great help friend's
thank you