How Electric and Magnetic Fields work in Mass Specs
Electric fields and magnetics field act differently on particles:
Assume we will shoot ions at high speed through a field and separate them: All will have same energy, e.g., 10keV
But this means different velocities because E = 1/2mv2
1. Magnetic Fields Sort Ions according to mass:
Magnetic force = B e v, where B = field, e = charge, v = veloc. So force α veloc.
Compare Hydrogen and Deuterium:
Veloc. of H is 2 times greater (kinetic E = 1/2mv2)
Force on H is 2 times greater
Acceleration (a=F/m), 2 2 times greater (it’s 1/2 the mass)
But, greater v means less time in the field (factor of 2 ) And Displacement α t2, so this means 1/2 the displacement
Net effect: Displacement is 2 greater for H+ than for D+. Conclusion: Ions in a mag. field have circular paths:
m −5 B2r2
e = 4.825 ×10 units of e- charges))
V (B = mag field (Gauss), V = accel. voltage, e is charge (in integer

r2 α kinetic energy α veloc.2
r2 α mass
**Note that an ion with 2 times the mass and a double charge will follow the same path.
2. Electric fields sort ions according to kinetic energy alone:
Force depends on charge alone: Same force for H and D H accel. = 2 D accel.
Time in field: 2 times greater for D than for H But displacement = at2
Therefore: the greater time and slower accel. for D cancel out.
Conclusion: In an electric field, all ions with same velocity/energy take the same path. Electric fields can be used as “energy filters”
r = 2E (r = path radius, E = energy of ions, V = field voltage) Vsector
Utility: Collisions in imperfect vacuum slowed ions (need to filter out)