A charged particle in a cyclotron moves in a circle with radius 5mm. If the field in the cyclotron is 0.06 T and the velocity of the particle is 2.4x10^7, what is the charge-mass ratio of the particle?
Firstly, we should equate the centripetal force to the force on a moving charge using equations from our formula booklet: (force on a moving charge): F = Bqv(centripetal force): F = mv2/rmv2/r = Bqvwhen we cancel the 'v's' we get:mv/r = Bqmultiply both sides by r to get: Bqr = mvdivide through by m and divide through by 'Br' to get: q/m = v/BrThis now gives us an equation for the charge mass ratio (q/m) as: v/BrNow, substitute in your given values for v (velocity), B (magnetic field strength) and r (radius), ensuring you use the correct index form. 2.4x10^7 / (0.06 x 5x10^-3) = 8x10^10 = q/m
