- #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
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