an alpha particle and a proton moving with the same speed enter the same magnetic field region at right angles to the direction of the field. deduce an expression for the ration of the circular paths of the two particles.

force acting on a particle entering at right angle to the magnetic field is equal to: Bvq

and this is equal to the centripetal force of the particle due to its rotation = mv²/r

thus radius = r = mv/Bq

now easily the ratio can be derieved.