Is there really no meaning in potential energy and potential?
I have been told all my physics life that potential energy between two mass/charge has no meaning and only their difference has meaning. The same goes for electric potential, only the difference matter.
Perhaps I am not understanding it correctly, but before I talk about masses, let's talk about potential energy/potential associated with two charges.
I am not sure where had I seen it, but a long time ago I was presented with a problem like this. Let's say I have a +Q and a -Q. What is the potential energy between them?
The change in potential energy is the negative work done by the conservative force namely (vector sign and dot product got rid of, since the cosine 1)
$\Delta U = -\int_{a}^{b} k(Q)(-Q) \frac{1}{r^2} = -k(Q)(-Q) \left. \frac{-1}{r} \right |_{a}^{b} = -k(Q)(-Q) \left (\frac{1}{b} - \frac{1}{a} \right) $
Now I assume that I brought it from infinitely far, so that 1/a = 0
In that case I am left with $\delta U = \frac{kQQ}{b}$
Here are my questions
1) A long time ago, I saw a formula looking EXACTLY like what I just did there, but it doesn't concern with the change, it's just gives me the potential energy. Now the formula I remember was $U = -\frac{kQq}{r}$ where there is a negative. 565
I thought this formula already takes care of the signs? Or am I wrong?
2) Kinda the same concept. If I tell you some charge (not telling you the sign) has a electric field and you have another charge (which is the test particle, not telling you the sign again even though it is conventional to use + charge ) somewhere in that field. I tell you that the electric potential at that point (not the difference) is K (where K is positive number). What can you conclude, if anything? What if it were negative?
Suppose I tell you suddenly that the charges are the same signs, and I give you a location in which the electric potential is positive (I think it has to be). What does it mean?
EDIT: Let me also just clarify a bit that I was taught that electric potential (not difference, I stress again) is the work that someone does to bring a charge from infinity to some point whereever. In my book however, it's defined as $V = \int_{R}^{\infty} \vec{E} \cdot \vec{ds}$ 531