In the last stage the ions, all with the same charge and velocity, enter a region of uniform magnetic field B_o. The field is perpendicular to the velocity, so the ions follow circular paths.

F = qvB_o = mv²/r

The radius is r = mv/qB_o

Since v was given by E/B for the velocity selector, this is sometimes written as:

r = mE/qBB_o

Everything is the same for the ions except for mass, so the radius of each circular path depends only on mass. The ions are collected after traveling through half-circles, with the separation s between two ions being equal to the difference in the diameters of their respective circles.

s = 2r₂ - 2r₁ = (m₂ - m₁) v / qB_o