An electron in a trajectory motion between the center of two plates

• Alfaraj
In summary, the problem asks for the magnitude of the y-component of an electron's velocity after it passes between two plates with a high voltage potential difference. Using the conservation of energy equation and the formula for change in potential energy, we can find the final velocity in the x-direction. To find the final velocity in the y-direction, we can use the force acting on the electron due to the electric field between the plates and the time it takes for the electron to pass between them to calculate the acceleration and then the final velocity.
Alfaraj

Homework Statement

An electron with an initial velocity of 5.6x107 m/s in the x-direction moves along a trajectory that takes it directly between the center of two 20 cm x 20 cm plates separated by 1 cm. The plates are connected to a high voltage power supply so that the potential difference between them is 500V. What is the magnitude of the y-component of the electron’s velocity when it leaves the plates? (Answer in units of ANSWER x 107 m/s.)

Homework Equations

Kf + Uf = Ki + Ui
deltaU = q * delta V

The Attempt at a Solution

In this question I figured out the final velcity in the x-direction using the condervation of energy approach. I figured out the change in potential energy by multiplying the potential difference by the elementary charge. How do I obtain the final y-direction velocity?

The x component of the electron's motion is unaffected by the force on it due to the field between the plates. Use this to calculate how long the electron is between the plates.
The force on the electron due to the field acts in the y direction for this time and accelerates the electron in the y direction. Use this acceleration, and the time, to find the final y-direction velocity.

1. What is the physical significance of an electron in a trajectory motion between two plates?

The motion of an electron between two plates is significant because it demonstrates the effects of an electric field on a charged particle. This phenomenon is also crucial in understanding the principles of electricity and magnetism.

2. How does the electric field between the two plates affect the electron's motion?

The electric field exerts a force on the electron, causing it to accelerate towards the positively charged plate. As the electron travels towards the plate, it gains kinetic energy, which allows it to continue moving even after passing through the plate.

3. Can the electron's trajectory motion be affected by external factors?

Yes, external factors such as the strength of the electric field, the distance between the plates, and the initial velocity of the electron can all influence the trajectory of the electron.

4. What happens to the electron's motion when it reaches the other plate?

When the electron reaches the other plate, it experiences a force in the opposite direction, causing it to decelerate. Eventually, the electron will come to a stop and return to its original position between the plates.

5. How is the trajectory of the electron related to its energy?

The trajectory of the electron is directly related to its kinetic energy. As the electron accelerates towards the positively charged plate, its kinetic energy increases. On the other hand, as the electron decelerates and returns to its starting point, its kinetic energy decreases.

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