Cathode Ray Type Question - Electron being moved by horizontal plates

[ncm2]

Homework Statement

An electron is accelerated horizontally from rest in a television picture tube by a potential difference of 5710 V. It then passes between two horizontal plates 6.45 cm long and 1.24 cm apart that have a potential difference of 249 V (see figure below).


At what angle q will the electron be traveling after it passes between the plates?

Homework Equations

Potential Difference = -Ed

I have no idea really where I would start this other than that.

The Attempt at a Solution

I have been trying for about 40 minutes and I am right back where I was. I have no clue where to start.


Many thanks

 

[anathema]

for your question. This is a great opportunity to apply some basic principles of electromagnetism and kinematics.

First, let's consider the setup of the problem. The electron is accelerated horizontally by a potential difference of 5710 V. This means that the electron gains a certain amount of kinetic energy, given by the equation KE = qΔV, where q is the charge of the electron and ΔV is the potential difference.

Next, the electron passes between two horizontal plates with a potential difference of 249 V. This means that the electron will experience an electric field between the plates, which will cause it to change its direction. We can use the equation Potential Difference = -Ed to calculate the electric field between the plates.

Now, let's consider the forces acting on the electron. The electric force, given by F = qE, will act on the electron due to the electric field between the plates. Additionally, there will be no other forces acting on the electron, so it will move in a straight line in the absence of any external forces.

Using the principles of kinematics, we can calculate the angle at which the electron will be traveling after it passes between the plates. We know that the electron will experience a constant acceleration due to the electric force, so we can use the equation v^2 = u^2 + 2as to calculate its final velocity after passing between the plates. Here, u is the initial velocity (which is zero since the electron starts from rest) and a is the acceleration.

Once we have the final velocity, we can use basic trigonometry to calculate the angle at which the electron will be traveling. We know that the electron will have a horizontal velocity component and a vertical velocity component, and the angle between these two components will be the angle at which the electron is traveling.

I hope this helps you get started on the problem. If you need more help, please don't hesitate to ask. Good luck!

 

[baba89]

for your question! I understand that this problem may seem daunting at first, but with a little bit of knowledge and practice, you can definitely solve it. Let's break down the problem step by step and see if we can come up with a solution together.

First, let's start with the basics. We know that the electron is being accelerated by a potential difference of 5710 V and is then passing through two horizontal plates with a potential difference of 249 V. From the equation given, we can see that potential difference is equal to -Ed, where E is the electric field and d is the distance between the plates.

Next, let's consider the forces acting on the electron. Since it is being accelerated by the potential difference, we know that there must be an electric field present. The electric field is directed from the positive plate to the negative plate, and since the electron has a negative charge, it will experience a force in the opposite direction, towards the positive plate.

Now, let's think about the motion of the electron. Since it is being accelerated, we know that it will have a non-zero velocity after passing through the plates. The direction of this velocity will depend on the angle at which the electron enters the plates and the strength of the electric field.

To find the angle at which the electron will be traveling after passing through the plates, we can use the concept of work-energy theorem. This theorem states that the work done on an object is equal to the change in its kinetic energy. In this case, the work done on the electron is equal to the product of the electric force (qE) and the distance it travels (d). This work will be equal to the change in kinetic energy of the electron, which can be calculated using its final velocity and mass.

Now, we have all the necessary information to solve for the angle at which the electron will be traveling after passing through the plates. We can use trigonometric functions to relate the velocity and angle, and then solve for the angle using the equation we derived from the work-energy theorem.

I hope this explanation helps guide you in solving this problem. Remember, as a scientist, it's important to break down complex problems into smaller, more manageable steps. Keep practicing and don't be afraid to ask for help if you get stuck. Good luck!