# Talk:Electric potential energy

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## Negative Stored Energy in QM?

I find the last paragraph of the section on Stored Energy to be a bit misleading. The fact is that two oppositely charged particles held in close proximity will have less energy than two oppositely charge particles held infinitely far apart. However, both energies are formally infinite for point particles. This has nothing to do with quantum mechanics. Defining a single charged point particle to have zero energy is the quantum mechanics, and is a good introduction to the idea of renormalization. If such a paragraph were included, it would be nice to point out such subtleties, rather than cloud matters by saying the previous equation isn't true. 70.253.79.237 (talk) 18:19, 8 February 2009 (UTC)

In the context of an article about electrostatic potential energies, the final paragraph seem likely to confuse a lot of non-experts, so I have removed it as part of a general clean-up of this article (RGForbes (talk) 01:38, 15 April 2009 (UTC))(Richard)

## mass

Seems like this article deals with the basics, a point charge, but doesn't advance to include charges with mass. What do you think?   Thanks, Daniel.Cardenas (talk) 18:04, 16 May 2009 (UTC)

## Sign of energy

I am somewhat confused by the sign of energy in an electrical field. Say we have two oppositely charged ions. My naive thinking is: the energy of the system is U = q1*q2/r12 < 0; but it can also be U = \integral |E|^2 dr^3 >0 (according to the last section of this article)

Why the sign of U is different? or in another word, what I am missing here? —Preceding unsigned comment added by 128.219.49.9 (talk) 15:52, 7 July 2010 (UTC)

## Energy in electronic elements

I think that the equation for "The total electric potential energy stored in a capacitor" is wrong... I don't see how V squared is equal to Q. — Preceding unsigned comment added by Crococo (talkcontribs) 11:31, 9 August 2011 (UTC)

It does not say that.--Patrick (talk) 11:41, 9 August 2011 (UTC)

## Formula for the point charge distribution is obviously wrong.

the distance between each charges needs to be calculated for every singe charge, not just between the ith and the qth charge, whatever that even means.— Preceding unsigned comment added 17 August 2011 (UTC)

I removed this messy part and added a clarifying remark.--Patrick (talk) 05:01, 17 August 2011 (UTC)

## Intro

Why is the formula for the electric potential energy given in the intro section only to have it repeated later in the article? Plus the explanation that follows the formula doesn't have much to do with the formula itself. I suggest deleting the the formula as to reduce the clutter to this article. — Preceding unsigned comment added by Pprrff (talkcontribs) 04:08, 17 August 2011 (UTC)

That makes two of us who thought this. Okay, I decide to be bold and remove it, unless somebody stenuously objects. Formulas in ledes, unless that article is about the formula itself, are not a good idea. SBHarris 02:28, 18 August 2011 (UTC)
Re-added the equations because they were very helpful references for students going through the article for the first time. Even if they are just a reference, they were useful later in going through the rest of the article. If there is another location that is better to put them, feel free to move them. But there is nowhere else in the article that shows they are all equal. — Preceding unsigned comment added by FrozenMan (talkcontribs) 19:54, 3 October 2011 (UTC)

## Definition

For the one point charge the definintion we currenty have is: For one point charge q in the presence of an electric field E due to another point charge Q, the electric potential energy is defined as the negative of the work done to bring it from the reference position r_ref to some position r

Is it really the negative of the work? On the article the equation starts with the negative of the work but U(r_ref) - U(r) are also changed. When you get to the integral what you have is that the potential energy is the work to bring the charge from infinite to the r point.

So what I think is that the definition should be: For one point charge q in the presence of an electric field E due to another point charge Q, the electric potential energy is defined as the work done to bring it from the reference position r_ref to some position r

Am I missing something? Where is that little thing that I am unable to see or is it simply that the article is wrong?

--IngenieroLoco (talk) 20:37, 17 June 2012 (UTC)

Ok I just changed that part of the article to make it more coherent and understandable. --IngenieroLoco (talk) 17:49, 18 June 2012 (UTC)

## Proof of Energy stored in an electrostatic field distribution

How do we get from this step:

 {\displaystyle {\begin{aligned}U&=\overbrace {{\frac {\varepsilon _{0}}{2}}\int \limits _{{}_{\text{ of space}}^{\text{boundary}}}\Phi \mathbf {E} \cdot d\mathbf {A} } ^{0}-{\frac {\varepsilon _{0}}{2}}\int \limits _{\text{all space}}(-\mathbf {E} )\cdot \mathbf {E} \,dV\\&=\int \limits _{\text{all space}}{\frac {1}{2}}\varepsilon _{0}\left|{\mathbf {E} }\right|^{2}\,dV.\end{aligned}}}

... to this step?

 So, the energy density, or energy per unit volume ${\displaystyle {\frac {dU}{dV}}}$ of the electrostatic field is: ${\displaystyle u_{e}={\frac {1}{2}}\varepsilon _{0}\left|{\mathbf {E} }\right|^{2}.}$

The integral on top is a definite integral with constants as its limits - can we really apply the fundamental theorem of calculus here? The ${\displaystyle U}$ on top doesn't depend on position, whereas the ${\displaystyle U}$ in the expression ${\displaystyle {\frac {dU}{dV}}}$ does.

Intuitively, the step on top shows that total electrostatic potential energy in the universe is proportional to integral of the squared magnitude of the electric field everywhere, but the step below is saying that the energy density at any given point is proportional to the squared magnitude of the electric field there, which seems to be a stronger claim.

Yaxy2k (talk) 14:54, 1 December 2013 (UTC)

## Explanation for the layman

This article does no favors to the layman. I'm suggesting the following, incorporate it into the article if you like it

Suppose I'm able to hold a negative charge on my left hand, and another negative charge on my right hand. This configuration of charges seems to have no energy because there is no movement. But if I let go the one on my right hand, it would accelerate, thus gaining energy. This energy couldn't have been created (conservation of energy), so we say that it was already there somehow and we call it potential energy, the energy that the configuration has the potential to release. This idea is supported by the fact that: 1. this exact configuration always releases the same energy 2. the energy that you need to assemble this configuration is always greater than or equal to the energy that it releases.

With the "the energy that the configuration has the potential to release" definition I would write something along the lines of

${\displaystyle U=\int _{R}^{\infty }\mathbf {F} \cdot d\mathbf {r} }$

That is, the potential energy of this configuration of charges is the work that one charge would do on the other if we let it evolve without any other constraints. --94.132.98.33 (talk) 10:58, 23 January 2016 (UTC)