I was explaining the construction of Thomson's apparatus for determination of specific charge for an exam today and suddenly something popped up: Consider 2 oppositely charged plates held using insulated handles (They're not connected to a battery). If an electron moving with a velocity v passes perpendicular to this field then it will experience a force eE causing it to accelerate towards the positive plate. Suppose v is such that the electron escapes the volume between the plates before it can reach the positive plate. Thus the electron leaving the area between the plates would have a greater kinetic energy because the magnitude of v vector would have increased. How can one account for this energy? The plates could not have lost any energy since they are not connected to a cell or allowed to move. And the net field outside the plate system would be zero from Gauss law. Then where did this extra energy come from?!