# How do you calculate the voltage between two charged nodes?

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1. Aug 29, 2015

### Cuppasoup

If:
1) you know the vertex and individual charge of each node and
2) voltage is the difference in electric potential energy between two nodes

How do you calculate the voltage in a vacuum?

2. Aug 29, 2015

### Staff: Mentor

Nodes where, vacuum where?

3. Aug 29, 2015

### Cuppasoup

I don't understand your question. 2 objects in space, each with an individual charge(in coulombs). How do you calculate the "tension" (in voltage)between the two charged entities?

By "where" do you mean, "what is the vertex of each node?"? If that's your question, shouldn't it be calculable with a formula?

Last edited: Aug 29, 2015
4. Aug 29, 2015

### Staff: Mentor

That question is much easier to understand than the original post.
Calculate the electric field everywhere (in most cases, to a good approximation: the sum of the fields of two point charges), integrate from one surface to the other.

5. Aug 29, 2015

### Cuppasoup

Okay, thanks for the help! By "Calculate the electric field everywhere," do you mean to calculate 2 individual matrices of "tension" depending on the charge and shape of the object and add them together to calculate the resulting electric field?

6. Aug 29, 2015

### Staff: Mentor

If the objects are not too close, that will give a reasonable approximation. If they are close, they will influence the charge distribution of the other object and things get complicated.

7. Aug 29, 2015

### Cuppasoup

Oh okay, I guess that means the distinction between "objects" is then blurred.

So how do I calculate an electric field matrix?

8. Aug 29, 2015

### Staff: Mentor

Two 1-meter objects with a distance of 0.5 meters between them are clearly different objects, but their charge distributions will influence each other significantly.
This is not a matrix, it is a vector field. If you can approximate the charge distribution as spherical, do that. Some other shapes might have analytic solutions, the general case can be treated with numerical methods.

9. Aug 29, 2015

### Cuppasoup

Ok, so to start off in 2D with a circle, if I were to calculate a vector field surrounding a charged "point" in the origin, is there a formula to calculate each vector by its coordinate in relation to the charge of the point?

10. Aug 29, 2015

### Staff: Mentor

In a two-dimensional world:
$$\vec E = \frac{q}{4 \pi \epsilon_0} \frac{\vec r}{r^2}$$
In a three-dimensional world:
$$\vec E = \frac{q}{4 \pi \epsilon_0} \frac{\vec r}{|r|^3}$$
Where q is the charge and r is the vector between charge and the point where you calculate the electric field.
Note that the charge should have some finite size, otherwise its potential is not well-defined.

11. Aug 29, 2015

### Cuppasoup

Excellent! Thanks!!