How Does an Electron Behave Between Parallel Conducting Plates?

[stanli]

Homework Statement

An electron is fired at a speed of v0 = 5.6 × 106 m/s and at an angle of θ0 = – 45° between two parallel conducting plates that are D = 2.0 mm apart, as in Figure P16.66. If the potential difference between the plates is ΔV = 100 V, determine (a) how close d the electron will get to the bottom plate and (b) where the electron will strike the top plate.
That is the exact question from the textbook. there is a diagram that shows the two plates and the electron starting in the middle of the two plates.

Homework Equations

I'm assuming you'll need Ei=Ef or some sort of projectile motion. I really don't even know that.

The Attempt at a Solution

I haven't the foggiest idea for part b, but for part a I attempted to do it like this and got an answer. I did Ei=Ef for the first part and set KE=electrical potential energy. Then substituted (delta)v over D for E and was able to solve for E and get 50000 v/m and then solved the equation for d and got 1.79 x 10^-3 m. Is that ok? and please any help. I really need it badly.

 

[foxjwill]

Your method for part a) is correct.

For b), use the standard equations for projectile motions, but instead of using the acceleration due to gravity, use the acceleration due to the electric field.

 

[Moetasim]

I would approach this problem by first understanding the basic principles of electricity and projectile motion. I would then use the given information, such as the speed and angle of the electron, the distance between the plates, and the potential difference, to set up equations and solve for the unknown variables.

For part a, determining how close the electron will get to the bottom plate, I would use the equation for electric field (E=ΔV/d) to find the electric field strength between the plates. Then, I would use the equation for projectile motion to calculate the distance (d) that the electron will travel before it hits the bottom plate. It seems like you have approached this part correctly by setting the initial kinetic energy equal to the electrical potential energy and solving for d.

For part b, determining where the electron will strike the top plate, I would use the equations for electric field and projectile motion again to calculate the distance (d') that the electron will travel before it hits the top plate. This distance can be found by setting the final kinetic energy equal to the electrical potential energy. The angle at which the electron will hit the top plate can also be calculated using trigonometric functions.

Overall, it seems like you have approached the problem correctly, but it would be helpful if you could show your work or equations so that I can provide more specific feedback. Remember to always double check your units and use appropriate equations for each part of the problem.