Two charged particles of equal mass are sent into the same u

Two charged particles of equal mass are sent into the same uniform magnetic field. Particle 1 has a charge +q and a speed v, while particle 2 has a charge +4q and a speed 5v. The velocities of both particles are perpendicular to the magnetic field. If the period of particle 1’s motion is 1x10-3 s, what is the period of particle 2’s motion?

Solution

T = 2pi*m/qB

particle time period does not depends on velocity

T1/T2 = q2/q1

q2 = 4q1

1*10^-3/T2 = 4q1/q1

T2 = 2.5 x 10^-4 s