# What does positive U mean?

1. Mar 18, 2014

### jonathan.15

If a group of point charges as a whole, has positive potential energy, what does that mean? What will happen if the point charges are free to move?

2. Mar 18, 2014

### phinds

What kind of point charges are you talking about? Electrons? Ideal point charges? Something else?

Are you talking about gravitational potential energy or electrical potential energy ?

3. Mar 19, 2014

### nasu

Unless you specify the reference point for potential energy, it means nothing much.

4. Mar 19, 2014

### Philip Wood

Presumably the convention is the usual one that the PE would be taken as zero if the charges were 'infinitely' separated. In this case, a positive PE would mean that the electric field forces would do a positive amount of work on the particles if the particles were allowed to move apart. Is that enough to help you picture what will happen?

5. Mar 19, 2014

### jonathan.15

Yes I am referring to electric potential energy of a group of point charges, say 2 negative and 1 positive. This group of charges will have a net negative potential energy. What does this mean? What will happen?

6. Mar 19, 2014

### jonathan.15

I also don't know what is meant by ideal pint charges, I'm taking an introductory college E&M physics course so I assume they are ideal.

7. Mar 19, 2014

### Philip Wood

Will it? The total PE of the system will be
$$E_p = \frac{Q{_1}Q{_2}}{4\pi \epsilon_0 r_{1, 2}} + \frac{Q{_2}Q{_3}}{4\pi \epsilon_0 r_{2, 3}} + \frac{Q{_3}Q{_1}}{4\pi \epsilon_0 r_{3, 1}}$$
Here, $r_{1, 2}$ and so on are magnitudes of separating distances.
If two of the charges are negative and one is positive, then two of the terms in the sum will be negative and one will be positive, but I don't think you can deduce that the sum will be negative, as you haven't specified how large the charges are, or their separations.
As for what it means to say that the system has a net negative potential energy, please see my previous reply.

I don't think we can say what will happen unless we have more information about the charges and their separations.

Last edited: Mar 20, 2014
8. Mar 19, 2014

### Khashishi

Potential energy can have an arbitrary offset, so the fact that the energy is positive means nothing at all.

But, for systems of point charges, it is conventional to set the zero of energy to be the situation where the charges are infinitely far apart. In this case, a positive potential energy means that some charges are repelling each other and will fly apart unless somehow held. The system as a whole must be unstable.

9. Mar 22, 2014

### jonathan.15

Thank you guys for clearing things up. Also, I was assuming the charges were equally far apart from one another like at the vertices of an equilateral triangle and that they all had the same magnitude of charge. In which case the U would be negative