Potential Energy of an Electric Field

[jbunten]

Hi,

This should be quite a simple question but here goes:

My question is about the conservation of electrical potential energy. Say we have a conducting plate filled with a positive charge Q. If we place a small +ve charge q in its vicinity it will accelerate away as the charges repel each other, where has the potential energy in Q's Field "gone" that repelled q?

 

[malty]

Hi,

This should be quite a simple question but here goes:

My question is about the conservation of electrical potential energy. Say we have a conducting plate filled with a positive charge Q. If we place a small +ve charge q in its vicinity it will accelerate away as the charges repel each other, where has the potential energy in Q's Field "gone" that repelled q?

No where,the potential will always be there if the charge q is there.

The concept of a field classically is that any point charge 1 has potential to do some work. If another "test" charge is placed in the vicinity of charge 1 then the work that charge 1 does on the test charge will be the field potential at that point.
In a way a field is a kinda model of the charge another charge q3 would experience if placed at a certain point within the vicinity of charge q4.
Hand- wavey description, but hopefully it answers your question.

 

[jbunten]

Ok, that's quite a good explanation, however charge 1 must use energy to perform work on the test charge, where does this come from? or is there something I am conceptually not grasping?

 

[malty]

Ok, that's quite a good explanation, however charge 1 must use energy to perform work on the test charge, where does this come from? or is there something I am conceptually not grasping?

Energy must be conserved right. Potential is the ability the charge has to do work on another charge if placed nearby, but you may also look at it this way the charge q is always doing work but the work will only be noticed if another charge is placed in its vicinity.[*This is not strictly correct though because work is defined as the force by distance moved, as nothing has moved no work has or is being done*]
The charge will always have a finite amount of potential energy that will not change, but it will of course vary from point to point (remember it falls of to the square of the distance), at each point this potential should always be the same. Field lines are used to joins points of equal potential.