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In an electron velocity selector, we use a positively charged plate (with a slit) to accelerate the electrons which then go through the slit and into an area with an electric and magnetic field. If that charged plate accelerates the electrons before they reach the slit, wouldn't it slow the electrons down once they have gone through the slit and, therefore, the velocity of the electrons wouldn't be constant in the area where the electric and magnetic fields are?

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As explained here, there is no field outside a parallel plate capacitor with very big plates near the center. That is, there is only an electric field between both plates, and quite close to the edges of the plates.

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