# Quick Electric Potential Concept Question

## Homework Statement

Explain why the potential energy between a positive charge and a negative charge is <0

## The Attempt at a Solution

I honestly don't know, I've tried reading the text about electric potential and I just can't find anything on the subject.

If I'm grasping the picture correctly, you're considering the electric potential energy midway between a positive point charge and a negative point charge (each point charge being equal in magnitude). When dealing with point charges, the convention is to assume a zero potential energy at a point infinitely far away from the charges being considered. Think about how much work it would take to bring a positive point charge +q from a point infinitely far away (potential energy = 0) to the point midway between the positive and negative charges. How much work is done on the point charge +q by the negative point charge, how much work is done by the positive charge, and finally, what does the total work amount to?

If I'm grasping the picture correctly, you're considering the electric potential energy midway between a positive point charge and a negative point charge (each point charge being equal in magnitude). When dealing with point charges, the convention is to assume a zero potential energy at a point infinitely far away from the charges being considered. Think about how much work it would take to bring a positive point charge +q from a point infinitely far away (potential energy = 0) to the point midway between the positive and negative charges. How much work is done on the point charge +q by the negative point charge, how much work is done by the positive charge, and finally, what does the total work amount to?

Thanks for the help but I don't really think that has to do with the question. I have many questions on this homework dealing with what you mentioned, but for this question I need to literraly find why the electric potential between a positive & negative charge is 0.

Ahhh, "electric potential." You said potential energy. This doesn't change much of what I said however, seeing as the electric potential is simply the electric potential energy per Coulomb of charge. Similarly, just as we define a point infinitely far away from the charges in question to be of zero potential energy, we do the same for "electric potential." Consider the change in electric potential, or "voltage":

$$\Delta V = \frac{U_f}{q} - \frac{U_0}{q}$$

How can this equation amount to zero? Consider the change in electric potential energy "U" alone:

$$\Delta U_E = \frac{kqq'}{r_f}-\frac{kqq'}{r_0}$$

The initial electric potential energy goes to zero, as we've defined. To see that the final potential energy goes to zero, we simply add the potential energies gained by the point charge +q as it nears the mid-point between the stationary point charges. With q' and -q' as the stationary charges, we'd have:

$$U_f = \frac{kqq'}{r_{mid}} + \frac{kq(-q')}{r_{mid}} = 0$$

And so we can conclude that since the initial and final electric potential energies are both zero, the electric potential, or "voltage" must be zero as well.

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whoa, thats whey past anything we've learned, and it's still not right i don't think. It should be a lot easier than this, i'm in an introductory physics class. It is supposed to be potential energy, and it's supposed to be less than 0, not equal. Thanks for all your help though, really appreciated.

The only way you can bring a point charge +q from infinitely far away toward a negative point charge and positive point charge of equal magnitude, and end up with a "potential energy" less than zero is if the charge +q ends up closer to the negative point charge and further from the positive point charge. Conceptually speaking, if a point charge +q has an initial potential energy of U0= 0, and it moves toward a negative charge, its potential energy will decrease, causing a change in potential energy < 0. While it moves toward the positive charge, it's gaining potential energy, because that positive charge will push on the +q harder the closer it gets. Does that make sense?

The potential energy of a point charge is just U=qV, where q is the charge on the point charge, and V is the electric potential (as opposed to potential energy, which is U!) that charge is sitting in. And, to find the electric potential, V,(again, not energy) generated by a point charge, it is V = kq/r, where r is the distance from the point charge where you want to find the electric potential.

So, in this case we have 2 point charges, q1 and q2, each of them is sitting in the electric potential created by the other. So, we have q1 sitting in the electric potential created by q2, and vice versa. So lets calculate the potential energy of one of the point charges.

The Electric potential energy of charge q1 is U1=q1V, and V is the electric potential q1 is sitting in, which is created by q2. So V = kq2/r, where r is the distance from q2 to q1. Plugging in we have U1 = kq1q2/r.

And now for the key part. You must put the correct sign in front of the q's! So, we know that in our case one is positive and the other is negative, so what is the sign of the potential energy?

You do the same process for q2 if you like.