# Difference between Electric Potential energy and Potential energy

1. Feb 22, 2013

1. The problem statement, all variables and given/known data
A proton is released from rest in a uniform electric field of magnitude 8x10^4 V/m. After the proton has moved 0.5 meters
a) What is the change in electric potential?
b) What is the change in potential energy?
c) What is the speed of the proton?

2. Relevant equations
U(elec)=U(naught)+qEs
s=change in distance
q=charge of particle
E= electric field

3. The attempt at a solution
I'm more or less looking for clarification of the problem... on part a), do you think he means what is the change in electric potential energy?
If not, how does the electric potential change? Maybe I don't know the difference well enough.
In part b) if part a) is talking about electric potential energy of the particle, does the particle gain or lose mechanical potential energy?

2. Feb 22, 2013

### Simon Bridge

No. He has clearly asked for the change in electric potential.
You do need to go through your course notes for these definitions.
http://en.wikipedia.org/wiki/Electric_potential
http://en.wikipedia.org/wiki/Electric_potential_energy
What would "mechanical potential energy" be? If the particle loses potential energy from anywhere, it gains kinetic energy.

3. Feb 22, 2013

Okay, but if the electric potential is independent of the charge of the particle, and the electric field is uniform, wouldn't there be no change in the electric potential?
U(elec)=qV ==> V=U/q
I guess I am confused why he asked a) before b), because to solve it, U=qEs, and V=U/q.
So in this case V=Es? I just don't understand why there would be a change in electric potential in an infinite uniform electric field...

4. Feb 22, 2013

### Simon Bridge

The field is the gradient of the potential.

You should have something like $\vec{E}=\vec{\nabla}V$ in your notes.
If the gradient is a constant - what is the function?