Uniform Electrical potential energy

[ysmin55555]

Can someone explain the math of how potential energy travels from higher potential energy to lower potential energy (PE) along a uniform electric field?

I understand that in order for the point charge to move, gaining kinetic energy, it will lose potential energy. But using the equation PE=qdeltaXE, Q is positive, delta X is position and E is positive. So what am I missing to quantitatively show that potential energy is decreasing?

 

[Dale]

delta X is position

$\Delta x$ is change in position, which is negative in your example.

 

[Chandra Prayaga]

Your question can be more general. In one dimension:
the work done is dW = F Δx.
If the force is conservative, the potential energy is defined as ΔU = - ΔW = - F Δx
The force is F = - ΔU/Δx
So the force is in the direction of decreasing potential energy. That only says that the acceleration is in the direction of decreasing potential energy, not that the particle moves in the direction of decreasing potential energy. For example, the particle could be given an initial velocity in the direction of increasing potential energy (you could throw a ball up), and it would slow down because the force is opposite to the direction of motion.
The electrostatic force is a particular example of this, with F = qE.

 

[sophiecentaur]

how potential energy travels from higher potential energy to lower potential energy

That's not the way to discuss energy, imo. A system / object may move m(or just change) in such a way as to reduce the Potential Energy but the PE hasn't actually moved. A possible exception to that statement could be throwing a coiled spring across a room. In that case you could say that the PE of the coiled spring has moved but I don't think that would take you anywhere useful.

 

[Chandra Prayaga]

There was that problem in the language of ysmin55555. As sophiecentaur says, the potential energy does not move anywhere. It is the particle that accelerates towards lower potential energy.