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How can I derive the equation for Coulomb Potential V(r) from the laplace's equation for electrostatic potential? $\nabla^2\psi=0$ (assuming spherical symmetry) I have no idea how i should start.

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  • $\begingroup$ Isn't this done in textbooks on the subject of E&M? $\endgroup$ – Kyle Kanos Feb 14 '17 at 11:07
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\begin{align} \nabla^2 V&=0\\ \frac{1}{r^2}\frac{d}{dr}\left(r^2\frac{dV}{dr}\right)&=0\, ,\\ r^2\frac{dV}{dr}&=K\, ,\\ \vec E=-\hat r\frac{dV}{dr}&=-\hat r\,\frac{K}{r^2}\, . \end{align} The intermediate steps you can sort out by yourself.

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