Consider a mass spectrometer. The ions produced are accelerated across a potential V.
Now, the kinetic energy of an ion with charge q is given by qV. When it enters the analyser with electric field strength E (orthogonal to the trajectory), the radius of the trajectory is given by
r = 2K/qE, where K is the kinetic energy.
Substituting with qV, we get
r = 2V/E
The mass and charge terms disappear! So how exactly is this a kinetic energy analyser? Because as per this equation, all ions, irrespective of charge, mass and kinetic energy must have the same trajectory. Where is the flaw in my reasoning?