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Homework Statement
Hello, I have to calculate the self-energy of an uniform charged electron with radius R. The distributed charge is e.
Homework Equations
The SE is given as:
[itex] E=\frac{1}{2}\int dV \int dV' \frac {\rho(\vec r)\rho(\vec r')}{ |\vec r - \vec r'|}[/itex]
according to the problem sheet.
The Attempt at a Solution
Since it's uniformly charged I guess [itex] \rho(\vec r)=\rho(\vec r')=\frac{e}{(4/3)\pi R^3}[/itex]
And from here I'm stuck, I tried to evaluate the (ugly) integral: [itex] \int_{0}^{2\pi} \int_{0}^{2\pi} \int_{0}^{\pi} \int_{0}^{\pi} \int_{0}^{R} \int_{0}^{R} \frac{e^2r'^2r^2sin(\theta')sin(\theta)}{2[(4/3)\pi R^3]^2\sqrt{(r-r')^2+(\theta-\theta')^2+(\phi-\phi')^2}} \, drdr'd\theta d\theta' d\phi d\phi' [/itex] (In spherical coordinates.)
But maple just crashed when I put it in.
What am I doing wrong? Did I misunderstand the meaning of the prime? (Can I set [itex]\vec r' = \vec 0 [/itex]?)
Any hints are very appreciated.
Kind regards Alex