It is desired to make an E velocity selector with uniform, static, crossed, electric and magnetic fields over a length L. If the

It is desired to make an E × В velocity selector with uniform, static, crossed, electric and magnetic fields over a length L. If the entrance and exit slit widths are ∆x, discuss the interval ∆u of velocities, around the mean value u = cE/B, that is  transmitted by the device as a function of the mass, the momentum or energy of  the incident particles, the field strengths, the length of the selector, and any other  relevant variables. Neglect fringing effects at the ends. Base your discussion on the practical facts that L ~ few meters, E_max ~ 3 ×10⁶ V/m, ∆x ~ 10^-3-10^-4 m, u ~ 0.5-0.995c. (It is instructive to consider the equation of motion in a frame moving at the mean speed и along the beam direction, as well as in the laboratory.)