# Unreasonable answer for acceleration of an electron in field

• yungquark
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.

## 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

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).

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?

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.