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## Homework Statement

In classical electrodynamics, the scalar field [itex]\phi(r)[/itex] produced by an electron located at the origin is given by the Poisson equation

[itex]\nabla^2\phi(r) = -4\pi e\delta(r)[/itex]

Show that the radial dependence of the field is given by

[itex]\phi(r) = \frac er[/itex]

## Homework Equations

I'm not really sure if this is right, but this is what I found on wikipedia. I've never learned about this ∇^2 thing in a math class.

[itex]\nabla^2 \phi =\frac {\partial^2 \phi}{\partial r^2} + \frac 1r \frac {\partial \phi}{\partial r}[/itex]

## The Attempt at a Solution

Plugging in e/r for phi, you get:

[itex]\nabla^2 \phi = \frac {2e}{r^3} - \frac {e}{r^3} = \frac {e}{r^3}[/itex]

which isn't even close to the equation given in the problem. I am so lost, please help.