# Speed of a proton through potential difference

In summary, the speed of a proton that has been accelerated from rest through a potential difference of -1000V is 1/2mpv2.

## Homework Statement

What is the speed of a proton that has been accelerated from rest through a potential difference of -1000V?

## Homework Equations

ΔV=potential difference
V=U/q
Conservataion of energy
U=qEd (d is distance the proton is moving...i think)

## The Attempt at a Solution

Here is my thought process with this problem:
ΔV=-1000V this means the change in electric potential is (-), doesn't tell us what V(initial) or V(final) is, but we know the difference between them is 1000
I know that V=U/q
For the proton going through this potential difference it follows conservation of energy:
Ki+Ui=Kf+Uf→0+qEd=1/2mpv2+0→qEd=1/2mpv2
here is where I get stuck...
it looks to me like we have one equation and two unknowns
the equation being:qEd=1/2mpv2
the unknowns: E and v
And I guess I am not even sure if Uf=0.

Are you familiar with the conversion between eV and Joules? And in problems like this, usually you would assume the particle starts at rest, unless stated otherwise.

You do not need E or d, you were given the potential difference.

berkeman said:
Are you familiar with the conversion between eV and Joules? And in problems like this, usually you would assume the particle starts at rest, unless stated otherwise.
I am not familiar with this.

Orodruin said:
You do not need E or d, you were given the potential difference.
So we can then say ΔV=U/q=qEd/q=Ed? that's all I am seeing from this. There may be another equation I am not remembering that relates potential difference to potential energy...

ahh, are you saying that ΔV=U/q can be solved so U=qΔV and in this case everything is known?
then the equation:
Ki+Ui=Kf+Uf→0+Ui=(1/2)mv2+0→qΔV=(1/2)mv2 and then we can solve for v? That makes sense

Last edited:
So we can then say ΔV=U/q=qEd/q=Ed?
You really cannot because nowhere in the problem is it stated that there is a constant field. You are just complicating your life by introducibg it at all. The first equality is all you need and all you can really say based on the provided information.

Orodruin said:
You really cannot because nowhere in the problem is it stated that there is a constant field. You are just complicating your life by introducibg it at all. The first equality is all you need and all you can really say based on the provided information.
the first equality being ΔV=U/q?

## What is the speed of a proton?

The speed of a proton is approximately 2.18 x 10^6 meters per second.

## What is potential difference?

Potential difference is the difference in electric potential between two points in an electric field.

## How does potential difference affect the speed of a proton?

The speed of a proton is directly proportional to the potential difference. As the potential difference increases, the speed of the proton also increases.

## What is the formula for calculating the speed of a proton through potential difference?

The formula for calculating the speed of a proton through potential difference is v = √(2qV/m), where v is the speed in meters per second, q is the charge of the proton, V is the potential difference in volts, and m is the mass of the proton in kilograms.

## How is the speed of a proton through potential difference related to electric fields?

The speed of a proton through potential difference is related to electric fields because the electric field provides the potential difference that accelerates the proton and determines its speed.

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