Electric field in stored charges

[lluke9]

Okay, say we have one positive point charge, and one negative point charge.
Their charge values are exactly opposite (q and -q).
And say we place them a certain distance apart and hold them there, maybe creating something like a point-charge capacitor. These point charges can hold and transfer charge; they're kind of like charged spheres, but I just wanted to call them points for simplicity's sake. I was also afraid that the thread would descend into trivialities.Now, I have a few questions based on this setup:
How would you calculate the voltage difference between them, knowing just the charge and distance between (I ran into a divide by zero issue)?
Would the electric field be constant between them, like a capacitor?
If I were to connect them with a conductive wire, is that same electric field transferred through that wire?I drew up a little illustration in paint to make it clearer...
http://i.lulzimg.com/f3d5f9de2e.png

 

[Antiphon]

The voltage is infinite since the fields diverge at the charges. The usual way to do this is define a zero voltage point (say between the two) and then the voltage at any point (except at the charge) is the integral of E.dl between the two points.

You don't get infinities for capacitors because there aren't point charges on the plates of a (mathematical) capacitor, there is a surface charge distribution. You can integrate your way right into that without an infinity.

 

[lluke9]

The voltage is infinite since the fields diverge at the charges. The usual way to do this is define a zero voltage point (say between the two) and then the voltage at any point (except at the charge) is the integral of E.dl between the two points.

You don't get infinities for capacitors because there aren't point charges on the plates of a (mathematical) capacitor, there is a surface charge distribution. You can integrate your way right into that without an infinity.

I don't really understand this integral stuff. as I haven't taken calculus or AP Physics C yet, sorry...

Is there a simpler explanation?


Also, why is there a constant electric field between capacitor plates?
If I put them EXTREMELY far away from each other, there's no way the field in between = field near a plate?

 

[Antiphon]

The fields in a capacitor are only uniform if the plates are much larger than the separation.

The simple explanation is this.

You compute the voltage between two places by measuring how hard it is (i.e. how much work it takes) to move a charge from the first place to the second place.

In your example, you would put a tiny charge halfway between the two main charges. This is the first point and we will "reset the work counter" here and call it zero.

As you move the test charge toward the similar charge, it will take work. And the closer you get to the similar charge the harder it will push back.

The voltage can be directly measured by the work it takes to get the charge to its destination. Since the forces become unbounded as you near the main charge, so then does the voltage.