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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.

User Adriel
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2 Answers

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Final answer:

The speed of the electron, when it reaches the bottom plate, can be determined using the equation vf = vi + at, where vf is the final velocity, vi is the initial velocity, a is the acceleration, and t is the time taken.

Step-by-step explanation:

Given a proton released from rest just above the lower plate with a certain speed and an electron released from rest just below the upper plate, we can determine the speed of the electron when it reaches the bottom plate. When the electron is released, it will experience an electric force due to the electric field between the plates. This force will accelerate the electron and increase its speed as it moves toward the bottom plate.

The electric force (Fe) experienced by an electron in an electric field is given by Fe = qeE, where qe is the charge of the electron and E is the electric field strength. The acceleration (a) of the electron is given by ae = Fe/me, where I is the mass of the electron.

Using the equation vf = vi + at, where vf is the final velocity, vi is the initial velocity (0 as the electron starts from rest), a is the acceleration, and t is the time taken, we can find the speed of the electron when it reaches the bottom plate.

User Neil Danson
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Answer:

v = √ 2e (V₂-V₁) / m

Step-by-step 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

User TheNeil
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