A proton of mass is released from rest just above the lower plate and reaches the top plate with speed . An electron of mass is released from rest just below the upper plate. Calculate the speed of the electron when it reaches the bottom plate, in terms of , , , and physical constants, as appropriate. Ignore gravitational effects.

  v = √ 2e (V₂-V₁) / m

Explanation:

For this exercise we can use the conservation of the energy of the electron

At the highest point. Resting on the top plate

         Em₀ = U = -e V₁

At the lowest point. Just before touching the bottom plate

        Emf = K + U = ½ m v² - e V₂

Energy is conserved

         Em₀ = Emf

          -eV₁ = ½ m v² - e V₂

           v = √ 2e (V₂-V₁) / m

Where e is the charge of the electron, V₂-V₁ is the potential difference applied to the capacitor and m is the mass of the electron

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