- #1
Bassalisk
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Homework Statement
In an imaginary sphere with radius R, there exist uniformly distributed space charge ρ. Find the potential in all points in space, bounded by this sphere. (r<R). Dielectric is air. ******Must use Poisson or Laplace equation******
Homework Equations
[itex]\nabla\cdot\nabla ={\Large -\frac{\rho}{\epsilon _{0}}}[/itex]
The Attempt at a Solution
I did everything, and I found that one of the constants is 0.
But I get stuck when trying to find the second constant.
[itex]\phi (r) ={\Large -\frac{\rho r^{2}}{6\epsilon _{0}}}+C_{2}[/itex]
I know that potential is constant on R. But I don't know how to use that. I am basically stuck here. I tried with some derivations, that equal 0 etc. But didn't get me anywhere.
I have the solution for the constant: [itex]C_{2}={\Large \frac{\rho R^{2}}{2\epsilon _{0}}}[/itex]
Can somebody help me?
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