A beam of ions passes undeflected through two parallel horizontal plates 1.5cm apart having a p.d of 3000v when a perpendicular magnetic field of 10-2T is applied and in the magnetic field alone beam is bent into a curve of radius 2m. Calculate the charge mass ratio of the ions

Answer 1

E = 3000 / 0.015 vols/meter
F of E field = Q E

F of Bfield = Q v B
if the forces balance then
Q E = Q v B
E = v B
3000 / 0.015 vols/m = v * 10^-2 Tesla
v = 2 * 10^7 meters/s (about 1/10 speed of light)
Then
m v^2/R = centripetal force = Q v B
so
Q/m = v / RB = 2*10^7 / 2*10^-2 = 10^9