# Confusion regarding Electric Potential Energy and Work

• Abu
In summary, the first formula states that the work done is negative because the small charge is displacing an area of higher electric potential. The second formula states that the work done is positive because the system (small charge and large charge) is being displaced.
Abu
Hi everyone.

I've been doing a lot of reading regarding electric potential and electric potential energy. Unfortunately, I have a lot of confusion regarding this topic, as I keep receiving different information. My main confusion is regarding the signs, positive or negative, of work and it's respective potential energy... as well as what is doing the work in the first place.
I have seen some people write the formulas of electric potential energy and work as:

W=-PE = -qΔV
And I've also seen people write it as:
W=PE = qΔV

To clarify my confusion, let's say that we have two positive charges that are fixed across from each other, with another smaller positive charge that is in between them, like this:

And we move the smaller positive charge to the right
If we go by the logic of the first formula, which states:
W=-PE = -qΔV
Then
1. The change in PE will be positive, because it is going from an area of lower potential to one of higher (closer to the large positive charge on the right)
2. The value for q will be positive because the small charge is a positive charge
3. The work done will be negative, according to the formula
4. The PE will also be positive because you will have -PE = -qΔV and the negative signs cancel each other out
Now my confusion is why is the work done negative? I am guessing, and correct me if I am wrong, that when the charge is moved closer to the right, the value for the electric field becomes larger to the point that overall the electric field is pointing to the left. As a result, since the charge's displacement is to the right and the overall electric field vectors point to the left, then the work done is negative. However, I'm not trying to turn this into a homework thread, but a similar problem showed that the answer for the work done was positive... which conflicts with my previous logic and what the formula above states.

If we use the second variation of the formula, which states:
W=PE = qΔV
Then
1. The change in PE will be positive
2. The value for q is still positive
3. The work done will be positive
I don't know which version of the formula is correct, or perhaps I should say I don't know what is doing the work on the small charge.

I know this is kind of a lengthy post, but it has been on my mind for a while now. I appreciate all feedback I receive on this. Thank you very much everyone. I can also add more diagrams if my question isn't clear.

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Abu said:
W=-PE = -qΔV
And I've also seen people write it as:
W=PE = qΔV
Both formulas are correct. The first is the work done by the system. The second is the work done on the system. Just pick one, use it consistently, and at the end check if your answer makes physical sense.

## 1. What is the difference between electric potential energy and work?

Electric potential energy is the energy a charged particle has due to its position in an electric field. Work, on the other hand, is the transfer of energy from one object to another through a force. In the context of electric potential energy, work is done when a charge moves from one point to another in an electric field.

## 2. How are electric potential energy and work related?

Electric potential energy is directly related to work. The change in electric potential energy of a charged particle is equal to the negative of the work done on that particle. This means that as work is done on a charged particle, its electric potential energy increases, and as work is done by a charged particle, its electric potential energy decreases.

## 3. Can electric potential energy be negative?

Yes, electric potential energy can be negative. This occurs when the electric potential energy of a charged particle decreases, meaning work was done by the particle. This can happen, for example, when a negatively charged particle moves towards a positively charged particle, and the electric potential energy of the system decreases.

## 4. Why is electric potential energy sometimes referred to as potential difference?

Electric potential energy is sometimes referred to as potential difference because it is a measure of the difference in potential energy between two points in an electric field. This difference in potential energy is what drives charged particles to move from one point to another, similar to how a difference in height drives objects to move from a higher to a lower point in a gravitational field.

## 5. How is electric potential energy measured?

Electric potential energy is measured in joules (J) in the SI system. It is calculated by multiplying the magnitude of the charge (q) by the electric potential (V) at a given point in an electric field. The formula for electric potential energy is U = qV. The unit of electric potential, volt (V), can also be written as joules per coulomb (J/C), further emphasizing the connection between electric potential energy and work.

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