Charged particles are fired into a magnetic field (perpendicular to the motion of the particles). Using Fleming’s left hand rule, a magnetic force acts centripetally – such that the charged particles exhibit circular motion.

By equating the magnetic force acting on each charge, with the equation for centripetal force, we have:

Bqv=mv^{2}/r (1)

Where B is the magnetic field strength

q is the charge of each particle

m is the mass of each particle

r is the radius of curvature of each particle (i.e. the radius of circular motion)

v is the speed of each particle.

Rearranging equation (1) for m, we have:

m=Bqr/v (2)

Equation (2) allows us to calculate the mass of ionised atoms, with a charge q related to the number of electrons each ion has gained/lost, assuming we can measure the radius and velocity of each particle. In practice, we would fire the ions through a florescent gas, so their circular motion becomes visible. The speed at which ions enter the magnetic field, v, can be adjusted using an electric field to accelerate the ions into the magnetic field.