A charged particle in a magnetic field goes round a circle at a rate set by the field and the particle alone, 28 GHz per tesla for an electron and 15 MHz per tesla for a proton, and a faster one simply goes round a bigger circle.
The force qvB is sideways to the motion, so it only turns the particle: the radius is mv/qB and the time for a turn 2πr/v = 2πm/qB, with the speed cancelling. A 100 eV electron in 1 mT circles in 3.4 cm, once every 36 ns. This is what lets a cyclotron give a particle a push every half turn, and a mass spectrometer sort ions by the radius of their path.
Only while the speed is small compared with that of light: as a particle nears it the mass grows and the rate falls (a 5 MeV electron is already some 10 times slower). The field must be uniform, and the particle’s own radiation, a few collisions with gas, and the electric field of its neighbours are left out.
Estimate with the rule, then check it against the calculator that models it properly.
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