# High and low potential

1. Feb 21, 2014

### derek181

in my physics text it states that a positive charge accelerates from regions of higher electric potential to regions of lower electric potential and a negative charge accelerates from regions of lower potential toward regions of higher potential.

Now my problem with these statements is that a negative charge has the greatest potential when located near a negative charge which seems to contradict those statements.

Can someone clarify this for me. Is this just a notation thing where someone defined high potential as always being the positive charge and a low potential as being a negative charge?

2. Feb 21, 2014

### Staff: Mentor

Note that they are talking about the potential of the field in which the charge is immersed.

Don't confuse potential with potential energy (although they are related, of course). The potential surrounding a negative charge increases with distance from the charge. Thus a negative charge placed in the field of another negative charge does move towards the region of greater potential.

But the potential energy of the two negative charges is greatest when they are close together.

3. Feb 21, 2014

### LikesIntuition

Potential increases as you move toward a positive charge. It decreases as you move toward a negative charge. Seeing as potential energy is your voltage times your charge, things still tend to move from higher to lower potential energy! The convention comes from the fact that we define aspects of a field from the perspective of a positive test charge.

Negative charges move from low potential to high potential (since the charge is negative, making the switch to potential energy tells us they move from high potential energy to low potential energy).

Hope that helps!

4. Feb 21, 2014

### derek181

I am still not following so we have a negative point charge labelled A and we have a negative test charge labelled B located somewhere out in the electric field of point A it is going to take more energy per coulomb of charge to move that negative test charge closer to A so therefor the potential increases as B is brought closer to A. Also the potential energy is going to be the greatest when B is close to A as it is capable of doing more work if released.

5. Feb 21, 2014

### derek181

Ok so high and low potential is defined as high potential being positive charge and low potential being negative charge due to how we defined the electric field. The electric field was defined by placing a small positive test charge and dividing out by that small positive test charge in coulombs law so electric field lines radiate outward from positive charge because if we placed a positive charge it would accelerate outward and field lines radiate inward to negative charges because a positive test would accelerate toward a negative charge. ahhh so how does this relate to potential?

6. Feb 21, 2014

### LikesIntuition

So, potential is the field-analogue of potential energy. Basically, we are looking at the significance of electric charge without needing to have actual interactions occurring to understand the nature of that charge.

Thus, potential is like looking at potential energy, without needing to have two charges. We only look at the potential at a point in space, not for a charge at that point in space, which would be potential energy. This is useful because it enables us to look at the significance of one charge (the voltage it creates at some point in space).

We do this by asking ourselves "what energy would a charge have if I placed it here?" That energy, divided by the charge we are imagining, is the electric potential at that point. That's why we have the unit "joule/coulomb." Furthermore, the charge we imagine is by convention a positive charge. We always ask "what would a positive charge do if I placed it here?" That's why field lines leave positive charges and end at negative charges, and why we have voltage increasing as we move closer to a positive charge, and decreasing as we go toward a negative. However, if we actually insert a negative charge and look at its energy, it will have potential energy U=qV. For changes in energy, this will be ΔU=qΔV. So, we know a negative charge will naturally go through positive changes in potential energy. It goes from low voltages to higher ones. This makes ΔV positive for the negative charge. However, q of the negative charge is negative, so qΔV is negative, making ΔU negative, as usual. Our convention still allows our charges to lose potential energy, as they intuitively tend to do through motion as long as an external force doesn't do work on them.

Does that help at all?

7. Feb 21, 2014

### derek181

So looking at points in space in an electric field right.... but how do you get an electric field without charges. Maybe can you explain in more general terms. Cant this be simply explained by the energy per charge to move a charge from one location to another location in an electric field. I don't like this whole convention thing because the way I described it in my previous post is correct. potentials are relative.

Now referring to part of your post. If you insert a negative charge (into an electric field created by another charge) and look at its energy, it will have potential energy u=qv (relative to another point in that electric field). Now that negative charge will go through positive changes in energy IF no external force is applied because that charge will move opposite to the direction of the electric field so delta V is positive and this will make delta U negative. So potential energy decreases as you move toward a positive charge. yeah that makes sense.

8. Feb 21, 2014

### derek181

ok I think I get it. So we always think in terms of a positive test charge. A positive test charge does not want to be at high potential ( as anything in this world) so it flows from high to low potential and so in turn a high potential would have to be created by a positive charge and low potential by a negative charge. so following that convention a negative charge flows from low to high potential.

Sorry for beating this thing to death but I just have to know the why's and ask a lot of questions to make sure I fully understand this.

9. Feb 21, 2014

### LikesIntuition

Yeah, you've got it! I'm not crazy about convention myself, but it does make things easier in many cases, such as describing things to other people. It's just EXTREMELY important, in my opinion, to remember that conventions are just conventions: they often don't increase our understanding of the world in a meaningful way. So your gag reflex to them is natural for a person who wants to really understand things, I think.

10. Dec 14, 2014

### mario9

what will be the convention of work done in moving a positive test charge from infinity to the point p midway between two charges of magnitude +q and -q.

11. Dec 14, 2014

### nasu

As the work done by the field zero, it does not make much sense to talk about its sign, does it?