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Poisson equation for the field of an electron
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[QUOTE="Keonn, post: 5000047, member: 541774"] [h2]Homework Statement [/h2] 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] [h2]Homework Equations[/h2] 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[B] [/B]class.[B][/B] [itex]\nabla^2 \phi =\frac {\partial^2 \phi}{\partial r^2} + \frac 1r \frac {\partial \phi}{\partial r}[/itex] [h2]The Attempt at a Solution[/h2] 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. [/QUOTE]
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Poisson equation for the field of an electron
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