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.

 

[sardar]

I would like to clarify a few things about the concept of electric field in stored charges. First, it is important to note that the electric field is a vector quantity that describes the electric force per unit charge at a given point in space. In this scenario, the electric field would be directed from the positive charge towards the negative charge.

Now, to address the questions posed in this setup:

1. How would you calculate the voltage difference between them, knowing just the charge and distance between (I ran into a divide by zero issue)?

To calculate the voltage difference between the two point charges, we can use the formula V = (kq)/r, where k is the Coulomb's constant, q is the magnitude of the charge, and r is the distance between the two charges. In this case, since the charges have opposite signs, the voltage difference would be negative and the electric potential energy would be released if the two charges were to come together.

However, it is important to note that at the point where the two charges are placed, the electric field would be undefined (hence the divide by zero issue) since the electric force would be infinite due to the extremely close proximity of the charges. This is known as a singularity and is a limitation of the point charge model. In reality, charges are not point-like and have finite sizes, so the electric field would be well-defined at all points.

2. Would the electric field be constant between them, like a capacitor?

The electric field between two point charges would not be constant. It would vary with distance and follow the inverse square law, meaning that the electric field strength would decrease as the distance between the charges increases. This is because the electric field is directly proportional to the magnitude of the charges and inversely proportional to the square of the distance between them.

3. If I were to connect them with a conductive wire, is that same electric field transferred through that wire?

If you were to connect the two point charges with a conductive wire, the electric field between them would no longer exist since the charges would neutralize each other. The electric field would then be transferred through the wire as an electric current. However, if the charges were to remain separate and connected by the wire, the electric field between them would still exist and the wire would experience a force due to the electric field.

In conclusion, the concept of electric field in stored charges is a complex one and cannot be fully described