Unreasonable answer for acceleration of an electron in field

In summary: Therefore, even with a small force, it can experience a large acceleration. This is one of the principles of Newton's second law of motion - a smaller mass will experience a greater acceleration for a given force. In summary, the conversation discusses a two-part question involving calculating the electric force on an electron when placed in an electric field and the resulting acceleration. The computation is found to be correct, but the magnitude of the acceleration seems unreasonable. It is explained that this is due to the small mass of the electron, which allows for a large acceleration even with a small force. The concept of comparing acceleration and speed is also clarified.
  • #1
yungquark
2
1

Homework Statement



Hello PF!

Got a two-part question involving calculating the electric force on a electron when placed in an electric field of 0.75N/C to the right, and the acceleration of said electron. Our values are E=0.75N/C, q=-1.6e^-19, m=9.1e^-31 (charge and mass of electron)

Homework Equations



For the force, F=Eq, for the acceleration, ma=Eq --> a=Eq/m

The Attempt at a Solution



Plugging numbers in gives a seemingly unreasonably small force (FE=1.2e^-19N) and unreasonably large acceleration (a=1.3e^11m/s^2). Is the value of the electrical field strength given too high? It seems so, as the acceleration is ~400x the speed of light. In another example we were given, E=1.1e^-8N/C, which gave a much more reasonable acceleration. I saw somewhere else on PF that the unreasonably high acceleration was plausible when applied through relativity and that the working was right (example was with a proton), but I'm convinced I've done this wrong. Any advice would be greatly appreciated. Thanks!

Apologies for any formatting errors; I have read over guidelines and will be stricter on these in future
 
Physics news on Phys.org
  • #2
Your computation is fine given the input. Why do you think it is an unreasonable result?

Note that you can only use this acceleration for non-relativistic speeds so it will quickly become non-applicable (faster than millisecond scale).

yungquark said:
It seems so, as the acceleration is ~400x the speed of light.
Stop right there! You absolutely cannot, I repeat cannot, compare an acceleration and a speed. They are different physical quantities with different physical dimensions (i.e., they are measured using different units).

In order to make an estimate of whether or not the classical approximation holds you need to involve a time scale, or estimate the time scales for which it holds (as I did above).
 
  • #3
Hello Orodruin,

Thanks for the quick response!

Orodruin said:
Your computation is fine given the input. Why do you think it is an unreasonable result?

I questioned it originally just due to the sheer size of the magnitude; we had an in-class example that worked out around 2000m/s^2, for instance. Our lecturer is very insistent on examining outputs to check for reasonable results. Thank you for dispelling my doubts!

Orodruin said:
Stop right there! You absolutely cannot, I repeat cannot, compare an acceleration and a speed. They are different physical quantities with different physical dimensions (i.e., they are measured using different units).

Also appreciate this, thank you. I find I'm still making basic errors like this and trying to iron them out.

Out of interest, how is it that such a small force can result in such a large acceleration?
 
  • #4
yungquark said:
Out of interest, how is it that such a small force can result in such a large acceleration?
The electron is very very light.
 

1. What is the acceleration of an electron in a field?

The acceleration of an electron in a field depends on the strength and direction of the field, as well as the mass and charge of the electron. It can be calculated using the equation F=ma, where F is the force on the electron, m is its mass, and a is its acceleration.

2. How does the acceleration of an electron in a field affect its motion?

The acceleration of an electron in a field can change the direction and speed of its motion. If the acceleration is in the same direction as the electron's velocity, its speed will increase. If the acceleration is in the opposite direction, its speed will decrease. If the acceleration is perpendicular to the electron's velocity, its direction of motion will change.

3. Are there any factors that can affect the acceleration of an electron in a field?

Yes, there are several factors that can affect the acceleration of an electron in a field. These include the strength and direction of the field, the mass and charge of the electron, and any other forces acting on the electron, such as friction or other electric or magnetic fields.

4. Can the acceleration of an electron in a field ever be unreasonable?

Yes, the acceleration of an electron in a field can be considered unreasonable if it is extremely high or low compared to what is expected based on the factors mentioned above. It can also be considered unreasonable if it causes the electron to exceed the speed of light, which is not possible according to the theory of relativity.

5. How does the acceleration of an electron in a field relate to other physical phenomena?

The acceleration of an electron in a field is closely related to other physical phenomena, such as electric and magnetic fields, electromagnetic radiation, and the behavior of particles in quantum mechanics. Understanding the acceleration of an electron in a field is crucial in many areas of science, including physics, chemistry, and engineering.

Similar threads

Acceleration of an electron due to Magnetic and Electric fields
    • Introductory Physics Homework Help
Replies
1
Views
1K
An electron & a proton are each placed in an electric field
    • Introductory Physics Homework Help
Replies
1
Views
2K
Electric and Magnetic field acting on an electron
    • Introductory Physics Homework Help
Replies
25
Views
4K
Movement of electron in an electric field
    • Introductory Physics Homework Help
Replies
10
Views
6K
Find the max speed so that an electron doesn't hit the plate
    • Introductory Physics Homework Help
Replies
3
Views
2K
Electron accelerated through a potential and magnetic field
    • Introductory Physics Homework Help
Replies
3
Views
2K
Net Electron Acceleration and Potential Energy
    • Introductory Physics Homework Help
Replies
9
Views
1K
Electric Field Force Exerted Vertically
    • Introductory Physics Homework Help
Replies
9
Views
7K
Motion of charge in electric and magnetic fields
    • Introductory Physics Homework Help
Replies
8
Views
1K
Find the magnitude of the electromagnetic force on electron?
    • Introductory Physics Homework Help
Replies
3
Views
1K

Hot Threads

Recent Insights

Back
Top