Electric Field between two opposite, gaussian distributed charged spheres

In summary: It sounds like you may need to find the total rho of the charge distribution before you can calculate the fields.
  • #1
Nick White
2
0
Hi,

I understand how to get the electric field between two spheres of uniform charge,
[tex]
\vec{E} = \frac{\rho \vec{d}}{3 \epsilon_0}
[/tex]
which is simplified because at a point [tex]\vec{r}[/tex], the vectors from each charge center combine to give the distance, [tex]\vec{d}[/tex], between centers (since [tex]\rho[/tex]'s can be factored).

So far, calculating this for two overlapping spheres of gaussian charge distribution seems non-trivial since you can't make this factorization and simply obtain an expression proportional to [tex]\vec{d}[/tex]...

Am I correct with the complexity of this problem, or is there some way more efficient to approach this problem?

I hope to use this electric field to model a harmonic oscillator (electron sphere oscillating around stationary ion sphere) and find a frequency...

Thanks
 
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  • #2
I think you have first to calculate which is the total rho of you 3D distribution.

This seems to be the sum of the two rho's you presented. After that I guess you will have to use integration over the whole space to get the field at point P = (x,y,z).

Best Regards,

DaTario
 
  • #3
DaTario said:
I think you have first to calculate which is the total rho of you 3D distribution.

This seems to be the sum of the two rho's you presented. After that I guess you will have to use integration over the whole space to get the field at point P = (x,y,z).

Best Regards,

DaTario

Thanks for the response DaTario.

I've started with that method - finding the field at a point P = (x,y,z) (point [tex]\vex{r}[/tex] in spherical) by integrating the charge from the positive distribution [tex]\rho_{+}=\rho_{0}exp(-(r^{2})/(2\sigma^{2}))[/tex] and then the negative distribution [tex]\rho_{-}=\rho_{0}exp(-(r-d)^{2}/(2\sigma^{2})), assuming [tex]d[/tex] is the displacement of the negative charge center along the z-axis for convenience, but i think it get hairy because these end up being factors for the vectors [tex]\vec{r}_{+}[/tex] and [tex]\vec{r}_{-}[/tex] when you sum the electric fields to get the total, in the overlap.

I was wondering if there's maybe a book problem like this, or even an article i could refer to...

NW
 

1. What is an electric field between two opposite, gaussian distributed charged spheres?

The electric field between two opposite, gaussian distributed charged spheres is the force experienced by a test charge placed at any point between the two spheres. This force is caused by the interaction of the electric charges of the two spheres.

2. What factors affect the strength of the electric field between two opposite, gaussian distributed charged spheres?

The strength of the electric field between two opposite, gaussian distributed charged spheres is affected by the magnitude of the charges on the spheres, the distance between the spheres, and the dielectric constant of the medium between the spheres.

3. How is the electric field between two opposite, gaussian distributed charged spheres calculated?

The electric field between two opposite, gaussian distributed charged spheres can be calculated using Coulomb's Law, which states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

4. What is the significance of the gaussian distribution in the electric field between two opposite, gaussian distributed charged spheres?

The gaussian distribution in the electric field between two opposite, gaussian distributed charged spheres refers to the distribution of the charges on the spheres. This distribution affects the shape of the electric field and can result in a more uniform electric field between the spheres.

5. How does the electric field between two opposite, gaussian distributed charged spheres impact the behavior of charged particles?

The electric field between two opposite, gaussian distributed charged spheres can cause charged particles to experience a force and move towards or away from the spheres, depending on the sign of their charge. This force can also cause the particles to accelerate, change direction, or remain at a constant velocity.

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