How do you calculate the voltage between two charged nodes?

In summary, calculating the voltage in a vacuum involves knowing the vertex and individual charge of each node. Voltage is the difference in electric potential energy between two nodes. To calculate the electric field in most cases, the sum of the fields of two point charges can be integrated from one surface to the other. The charge distribution can be approximated as spherical to simplify the calculation, and in a two or three-dimensional world, the electric field can be calculated using the formula: E = (q/4πε0) * (r/r^2 or |r|^3) where q is the charge and r is the vector between the charge and the point where the electric field is being calculated. It is important to note that the charge should have some
  • #1
Cuppasoup
6
0
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?
 
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  • #3
mfb said:
Nodes where, vacuum where?
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?
 
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  • #4
Cuppasoup said:
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?
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.
 
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  • #5
mfb said:
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.
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
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.
 
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  • #7
mfb said:
If they are close, they will influence the charge distribution of the other object and things get complicated.
Oh okay, I guess that means the distinction between "objects" is then blurred.

So how do I calculate an electric field matrix?
 
  • #8
Cuppasoup said:
I guess that means the distinction between "objects" is then blurred.
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.
Cuppasoup said:
So how do I calculate an electric field matrix?
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
mfb said:
This is not a matrix, it is a vector field. If you can approximate the charge distribution as spherical, do that.
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
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.
 
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  • #11
Excellent! Thanks!
 

Related to How do you calculate the voltage between two charged nodes?

1. What is the formula for calculating voltage between two charged nodes?

The formula for calculating voltage, also known as potential difference, between two charged nodes is V = k * (Q/r), where V is the voltage, k is the Coulomb's constant (9 x 10^9 N*m^2/C^2), Q is the charge of the two nodes, and r is the distance between the two nodes.

2. How do you determine the direction of voltage between two charged nodes?

The direction of voltage between two charged nodes is determined by the polarity of the charges. If the charges are of the same sign, the voltage will be positive and the direction will be from the higher potential node to the lower potential node. If the charges are of opposite signs, the voltage will be negative and the direction will be from the lower potential node to the higher potential node.

3. Can voltage be negative?

Yes, voltage can be negative. As mentioned in the previous answer, if the charges of two nodes are of opposite signs, the voltage between them will be negative. This indicates a flow of electricity from the lower potential node to the higher potential node.

4. How does distance affect the voltage between two charged nodes?

The voltage between two charged nodes is inversely proportional to the distance between them. This means that as the distance increases, the voltage decreases and vice versa. This relationship is described by the inverse square law, which states that the voltage is proportional to 1/r^2, where r is the distance between the two nodes.

5. Is voltage affected by the type of charge or material of the nodes?

Yes, voltage can be affected by the type of charge or material of the nodes. Different materials have different electrical properties, such as conductivity and permittivity, which can affect the voltage between them. The type of charge also plays a role, as positive and negative charges have different properties and interactions with each other.

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