Electron between two plates

Using the given information, we can determine that the electron travels a distance of 1 cm between the plates. Using the position equation, we can set the initial position to be midway between the plates (0.5 cm) and solve for the acceleration, which is equal to the electric field. In summary, the magnitude of the electric field between the plates is equal to the acceleration of the electron, which can be found using the position equation and the given information.
  • #1
Digdug12
15
0

Homework Statement


An electron is projected with an initial speed v_0 = 2.00×106 {\rm m/s} into the uniform field between the parallel plates in the figure (Intro 1 figure) . Assume that the field between the plates is uniform and directed vertically downward, and that the field outside the plates is zero. The electron enters the field at a point midway between the plates.
If the electron just misses the upper plate as it emerges from the field, find the magnitude of the electric field.
(length of plates = 2cm, distance between plates=1cm)

Homework Equations


F=eQ
y=.5at^2+V(t)+y(initial)



The Attempt at a Solution


Ok, so first I tried to force on the charge from the electric field, but I don't know the electric field. So then I tried the position equation to find Acceleration but I don't know the time it took to travel through the plates, I would be able to find that but I am not sure if the velocity in the x direction stays the same? (the direction parallel to the plates)
 
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  • #2
As you have said, the velocity in the x direction remains the same.
 
  • #3


I would approach this problem by first analyzing the given information and identifying what is known and what is unknown. From the given information, we know the initial speed of the electron, the length and distance between the plates, and the direction of the electric field. We also know that the electron just misses the upper plate, indicating that it follows a curved path within the electric field.

To solve for the unknown magnitude of the electric field, we can use the equation F = eQ, where F is the force on the electron, e is the charge of the electron, and Q is the electric field. Since the electron travels in a curved path within the electric field, we can also use the equation for centripetal force, F = mv^2/r, where m is the mass of the electron, v is its velocity, and r is the radius of the curved path.

To find the radius of the curved path, we can use the position equation y = 0.5at^2 + v0t + y0, where a is the acceleration due to the electric field, v0 is the initial velocity, and y0 is the initial position. Since the electron enters the field at a point midway between the plates, we can assume that its initial position is at the center of the plates. We also know that the electron exits the field just before hitting the upper plate, indicating that its final position is at the edge of the plates.

Using the given length and distance between the plates, we can calculate the radius of the curved path and then use it to solve for the unknown electric field. From there, we can use the known values and equations to verify our answer and make any necessary adjustments.

In conclusion, as a scientist, I would approach this problem by utilizing known equations and analyzing the given information to solve for the unknown magnitude of the electric field. I would also verify my answer using the given values and equations to ensure accuracy.
 

What is an "Electron between two plates"?

An "Electron between two plates" is a scientific concept that refers to the behavior of an electron when it is placed between two parallel plates that have opposite electric charges. This situation creates an electric field that affects the movement of the electron.

What is the significance of studying "Electron between two plates"?

Understanding the behavior of an electron between two plates is important because it helps us understand the fundamental principles of electricity and electromagnetism. This concept is also used in various applications such as electronic devices and particle accelerators.

How does an electron behave between two plates with the same charge?

If the two plates have the same charge, the electron will experience a repulsive force and will be pushed away from the plates. This will cause the electron to move in a curved path, away from the plates.

What happens to an electron between two plates with opposite charges?

Between two plates with opposite charges, the electron will experience an attractive force and will be pulled towards one of the plates, depending on the strength of the electric field. The electron will then accelerate towards the plate with the opposite charge.

How is the electric field strength between two plates related to the movement of an electron?

The electric field strength between two plates is directly proportional to the acceleration of the electron. This means that the stronger the electric field, the faster the electron will move between the plates.

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