Getting electric potential from charge density over whole sp

In summary, the conversation discusses how to find the electric potential in a space with a given charge density. The suggested approach is to solve the Poisson equation, but the specific form of the charge density is ambiguous. The conversation also mentions Gauss Law and Coulomb's law as potential methods for finding the electric potential.
  • #1
Thomas Rothe
1
0

Homework Statement


Let’s say I have got a charge density $\rho (x,y,z) = \cfrac{C}{x^2}$ with C a specific constant. I want to know the potential on every point in space. How can I get an expression of the electric potential in terms of position?

Homework Equations


Gauss law/coulomb's law probably

The Attempt at a Solution


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Let’s say I have got a charge density ρ(x,y,z)=Cx2'>ρ(x,y,z)=Cx2ρ(x,y,z)=Cx2 with C a specific constant. I want to know the potential on every point in space. How can I get an expression of the electric potential in terms of position?

Plotting the charge density we get of course infinite amount of planes with the same charge density each, along the x-axis. With this picture in mind we might guess that there are just x-components of the electric fields perpendicular to the planes, because of symmetry.

I think that this could be a key point (if I was right) in calculating the potential (or electric field) but I just can’t come up with a specific expression for that since I would have to consider all planes with specific charge density. Neither Gauss Law, Coulomb’s law or any other definition of potential/electric fields seems to be applicable.

Is there a simple way to calculate such a potential? (It actually doesn’t seems to be that hard)
 
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  • #2
Hi Thomas Rothe and welcome to PF.

Please use legible code for your equations, preferably LaTeX.
I would try to solve the Poisson equation, ##\nabla^2 \varphi=\rho(x,y,z)##. Is ##\rho(x,y,z)=C/x^2##? I can't tell for sure.
 

Related to Getting electric potential from charge density over whole sp

1. How do I calculate the electric potential from charge density over a whole space?

To calculate the electric potential from charge density over a whole space, you can use the formula V = k * q / r, where V is electric potential, k is the Coulomb constant, q is the charge density, and r is the distance from the charge. You will need to calculate the electric potential at every point in space and then add them together to get the total potential.

2. What units are used to measure charge density?

Charge density is typically measured in units of coulombs per cubic meter (C/m^3). However, it can also be measured in other units such as coulombs per square meter (C/m^2) or coulombs per cubic centimeter (C/cm^3).

3. How does charge density affect electric potential?

The higher the charge density, the greater the electric potential will be. This is because a higher charge density means there are more charges in a given space, which leads to a stronger electric field and therefore a higher potential.

4. Can electric potential be negative or zero?

Yes, electric potential can be negative or zero. Negative electric potential indicates that the electric field is directed in the opposite direction of the electric force. Zero electric potential means that there is no electric field present at that point.

5. How does distance from the charge affect electric potential?

The electric potential decreases as the distance from the charge increases. This is because the electric field weakens with distance according to the inverse square law. Therefore, the closer you are to the charge, the greater the electric potential will be.

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