# Electric Potential and Consv of Energy, Is this right?

## Homework Statement

A proton with an intial speed of 800,000m/s is brought to rest by an electric field.
What was the potential difference that stopped the proton.

## Homework Equations

Ki + qvi = Kf + qvf

k=.5mv^2

## The Attempt at a Solution

Voltage final = ?
vi = 800,000m/s
v2=0
q=1.60x10^-19
m=1.67x10^-27

ki=.5mv^2
=.5(1.67x10^-27)(800,000)
=6.68x10^-22j

Ki + qVi = Kf + qVf
Ki=-qVi
6.68x10^-22j=(-1.60x10^-19)Vi
-4.175x10^-3=Vi

Its seems weird cause Energy isnt really conserved :s

## The Attempt at a Solution

Last edited:

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gneill
Mentor
You forgot to square the velocity when you were working out the Kinetic Energy.

thank you very much, :)
answer makes more sense now V=-3340V

but why will the energy is conserved?
Isn't external force acting on proton?

gneill
Mentor
but why will the energy is conserved?
Isn't external force acting on proton?

The "system" is the proton in the electric field. Electric fields are conservative.

they are conservative ,,, but energy is only conserved only when internal conservative forces act on the system,

here (acc. to your system) external forces are also acting.
So: Δ(mechanical energy) = work done by external forces

gneill
Mentor
they are conservative ,,, but energy is only conserved only when internal conservative forces act on the system,

here (acc. to your system) external forces are also acting.
So: Δ(mechanical energy) = work done by external forces
What external forces would those be?

The "system" is the proton in the electric field. Electric fields are conservative.
in the electric field ...
So you mean that whatever is causing electric field is not a part of system, right?

then wouldn't electric force be an external force? ...???

gneill
Mentor
in the electric field ...
So you mean that whatever is causing electric field is not a part of system, right?

then wouldn't electric force be an external force? ...???
Is the Earth part of the system that contains its gravitational field? Must we abandon conservation of energy when a projectile mass arcs through the Earth's field?

but in that case we include earth in our system, dont we?

gneill
Mentor
but in that case we include earth in our system, dont we?
More like we ignore it for practical reasons since we consider its mass to be so great that it is unperturbed. It is included when necessary (celestial mechanics, for example), but taken as a whole, when everything is included, the gravitational field is still conservative with regards to potential.

Regarding this question, the electric field is presented as a constant background, just as we take the Earth's gravitational field to be a constant background for our 'lab' experiments.