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I'm trying to find the electric potential inside a thin (not charged) spheric conductor of radius R, containing a point charge of charge +q exactly in the center.
To do this, I'm trying to solve the differential equation [itex]\Delta V = 0[/itex] (harmonic). Together with the boundary condition [itex]V(R) = c[/itex].
From the null laplacian, one can obtain [itex]V(r) = -\dfrac{\alpha}{r} + \beta[/itex], but I'm lacking one boundary condition. Can this method be applied even when there's a singularity (i.e. [itex]V(0) = \infty[/itex])?
How does one solve this problem? What additional boundary conditions are there?
To do this, I'm trying to solve the differential equation [itex]\Delta V = 0[/itex] (harmonic). Together with the boundary condition [itex]V(R) = c[/itex].
From the null laplacian, one can obtain [itex]V(r) = -\dfrac{\alpha}{r} + \beta[/itex], but I'm lacking one boundary condition. Can this method be applied even when there's a singularity (i.e. [itex]V(0) = \infty[/itex])?
How does one solve this problem? What additional boundary conditions are there?