Path radius

Remembering, that for a circular path the centripetal force is given by mv2/r ... and that the force on a particle of charge e moving with speed v perpendicular to a magnetic field is Bev gives....

.........Bev = mv2/r ............. (1)

If the electron has been accelerated through a potential diffrence V, the energy of the electron is eV Joules. In that case....

.........mv2 = 2eV ............. (2)

At once .....Bev = 2eV/r

and ........ ...... v = 2V/Br...

Substituting for v2 in equation 2 gives....

m 4V2/B2r2 = 2eV

and ............r = [2mV/eB2/]0.5

The radus of the path is inversely proportional to the magnetic field strength B. This is the principle of the mass spectometer.