Particle dynamics question. Electron in electric field.

[Amahia11]

Hey, just need help with something here.

Say an electron is traveling in a narrow beam (from an electron gun) at a steady
speed of 5X10^-7 m/s.
They're directed into the space between two oppositely charged parallel plates 50mm apart and the p.d. on the plates is 2500V.
A fluorescent screen is positioned 300mm from the end of the plates at right angles to the plates so that the beam of electrons hits the screen after passing through the plates (parabolically).

How can we find the displacement of the spot on the screen (from the electrons) when the p.d of the plates is switched on?
Help much appreciated! thanks!

 

[Andrew Mason]

Hey, just need help with something here.

Say an electron is traveling in a narrow beam (from an electron gun) at a steady
speed of 5X10^-7 m/s.
They're directed into the space between two oppositely charged parallel plates 50mm apart and the p.d. on the plates is 2500V.
A fluorescent screen is positioned 300mm from the end of the plates at right angles to the plates so that the beam of electrons hits the screen after passing through the plates (parabolically).

How can we find the displacement of the spot on the screen (from the electrons) when the p.d of the plates is switched on?
Help much appreciated! thanks!

The speed of the electron cannot be 5 x 10^-7 m/s. Should that not be 5 x 10^7 m/s.?

I also think you need to know the dimensions of the plates. You need to determine how long the electrons are subject to the deflecting force (ie how long they take to pass through the plates.

AM

 

[Amahia11]

The speed of the electron cannot be 5 x 10^-7 m/s. Should that not be 5 x 10^7 m/s.?

I also think you need to know the dimensions of the plates. You need to determine how long the electrons are subject to the deflecting force (ie how long they take to pass through the plates.

AM

Absoloutely, sorry my mistake that is the right speed.

Yes, sorry again, the plates are 0.1 metres in length and the fluorescent screen is 30mm away. Can you help?

 

[Andrew Mason]

Absoloutely, sorry my mistake that is the right speed.

Yes, sorry again, the plates are 0.1 metres in length and the fluorescent screen is 30mm away. Can you help?

Are you sure about these dimensions? .1 m is 10 cm or 100 mm. Your initial question said the screen was 300 mm or 30 cm away. You now say it is 30 mm. or 3 cm. Which is it?Think of the electrons acquiring momentum in the direction of the electric force they experience when passing between the plates*. How is that momentum related to the electric force and the time over which the force acts? The duration of that force is a function of the time spent between the plates, which, of course, is a function of the electron's speed through the plates.

There are two deflection distances that need to be determined. First you have to determine how far the electrons have deflected in passing through the plates ie. from the time they enter the plates to the time they reach the end of the plates (ie. in the direction of the electric force between the plates, which is perpendicular to their original motion). How is this distance related to the force and time over which the force acts?

Second, once you have determined how much momentum the electrons acquire due to passing between the plates, you can determine how far they will move in that direction in the time it takes the electrons to go from the end of the plates to the screen.

The total deflection is the sum of these two distances.

AM* the momentum vector is actually opposite to the electric field vector since these are negatively charged electrons

 

[rwisz]

I can provide some guidance on how to approach this question. First, we need to consider the forces acting on the electron as it travels through the electric field between the two plates. The electric field will exert a force on the electron, causing it to accelerate towards the positively charged plate. At the same time, the electron's initial velocity will give it a horizontal component of motion, resulting in a parabolic path.

To find the displacement of the spot on the screen, we can use the equations of motion for a particle in a uniform electric field. We know the initial velocity of the electron (5X10^-7 m/s) and the magnitude of the electric field (2500V/50mm = 5X10^4 V/m). We can use these values to calculate the acceleration of the electron and then use the kinematic equations to determine the displacement of the electron after a certain amount of time.

Additionally, we need to consider the distance between the plates (50mm) and the distance from the plates to the screen (300mm) to determine the angle at which the electron will hit the screen. This angle will also affect the displacement of the spot on the screen.

In summary, to find the displacement of the spot on the screen, we need to consider the forces acting on the electron, the initial conditions of the electron's motion, and the geometry of the setup. I hope this helps in your understanding of particle dynamics and the behavior of electrons in an electric field.