I tried to understand: Free electrons that cross the capacitor static field change trajectories, so work is done, but the capacitor field rest unchanged forever. Where comes the new energy from?
Now I think at this scenario: the incoming kinetic electron starts to interact with the capacitor...
I can not turn off the field, because it comes from the electrons of one plate and the ions of the other plate, and their number is not changed, no matter how many free electrons cross this field.
When the electron pass between the plates of a polarized (ideal) capacitor, the electric field modifies the trajectory of this electron. One billion electrons can follow and the capacitor field will be unchanged. Some work is done. Where comes this energy from?
I try to choose the "cheapest energetic" way to deflect an electron, based on its known interactions. The electron has, also, a mass. Hypothetically, I could obtain same deflection as in previous case using this time gravitational attraction of another mass. How can this mass be compared with...
We can deflect a moving electron using an electric field or using a magnetic field. In order to obtain the same deviation, when the energy we should use is higher? Or, in other words, the "electric" or the "magnetic" property is stronger?