Bainbridge’s mass spectrometer, shown in the figure, separates ions having the same velocity. The ions, after entering through slits and , pass through a velocity selector composed of an electric field produced by the charged plates and , and a magnetic field perpendicular to the electric field and the ion path. Those ions that pass undeviated through the crossed and fields enter into a region where a second magnetic field exists, and are bent into circular paths. A photographic plate registers their arrival. We have to show that , where r is the radius of the circular orbit.

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Condition for velocity selection of charge ions using crossed electric and magnetic fields is that the Lorentz force be zero, i.e.

As and are ,

Therefore, criteria for velocity selection in the first part of the Bainbridge’s mass spectrometer is that

Ions of charge q that come out of the velocity selector with the electric and magnetic fields being E and B, respectively, will have speed

These ions after emerging out from the velocity-selector move in a uniform magnetic field , which is perpendicular to . The radius r of the circular orbit is determined by the centripetal force provided by the magnetic field on the moving charges,