An electron is released at the negative plate of a parallel plate capacitor and accelerates to the positive plate a) as the electron gains kinetic energy, does its electric potential energy increase or decrease? Why?
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What does the law of conservation of energy tell you?
To determine whether the electric potential energy of the electron increases or decreases as it gains kinetic energy, we need to understand the relationship between electric potential energy and kinetic energy in a parallel plate capacitor.
In a parallel plate capacitor, such as the one described in the question, there is an electric field between the plates that accelerates charged particles. The electric potential energy (U) of a charged particle in an electric field is given by the equation U = qV, where q is the charge of the particle and V is the electric potential difference across the plates.
When the electron is released at the negative plate and starts moving towards the positive plate, it is accelerated by the electric field. As it gains kinetic energy, its speed increases. The kinetic energy (K) of a moving particle is given by the equation K = (1/2)mv^2, where m is the mass of the electron and v is its velocity.
Now, to understand the change in electric potential energy, we need to consider the equation for work (W) in terms of electric potential energy and kinetic energy. According to the work-energy theorem, the work done on an object is equal to the change in its kinetic energy. Since the electron is accelerated from rest, the work done on it is equal to its final kinetic energy.
The work done on the electron is given by the equation W = ΔK = Kf - Ki, where Ki is the initial kinetic energy (zero in this case) and Kf is the final kinetic energy.
Now, the work done on the electron is also equal to the change in electric potential energy, which can be expressed as ΔU = Uf - Ui, where Ui is the initial electric potential energy and Uf is the final electric potential energy.
From the equation W = ΔU, we can equate the change in kinetic energy to the change in potential energy:
ΔK = ΔU
Since the initial kinetic energy is zero, the final kinetic energy is equal to the change in kinetic energy:
Kf = ΔK
Therefore, we can rewrite the equation as:
Kf = ΔU
As the electron gains kinetic energy (Kf increases), the change in electric potential energy (ΔU) must also increase to account for the work done on the particle. This implies that the electric potential energy of the electron increases as it gains kinetic energy.
In conclusion, as the electron gains kinetic energy while moving from the negative plate to the positive plate of a parallel plate capacitor, its electric potential energy increases.