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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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# Electric Field between two opposite, gaussian distributed charged spheres

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