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Math Help - whats the electric field and potential in an atomic nucleus

  1. #1
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    whats the electric field and potential in an atomic nucleus

    given total charge Q uniformly distributes in an atomic nucleus with radius R.
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  2. #2
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    Quote Originally Posted by szpengchao View Post
    given total charge Q uniformly distributes in an atomic nucleus with radius R.
    If you mean the external electric potential due to the atomic nucleus then I believe the answer is exactly the same as the electric field for a point charge at the nucleus centre. So if you are a distance Z from the nucleus centre ( Z>R) then the potential is

    \Phi_E = \frac{Q}{4\pi\epsilon_0 Z}

    If you need to show this what you need to do is perform a volume integration in spherical coords. Your density is \rho=3Q / 4\pi R^3, and the distance to the volume element is \delta = (r^2+Z^2-2rZ\cos\phi)^{1/2}. Then you want to evaluate
    <br />
\Phi_E = \frac{\rho}{4\pi\epsilon_0}\int_0^R\int_0^\pi\int_  0^{2\pi} \frac{r^2\sin\phi\,d\theta\,d\phi\,dr}{(r^2+Z^2-2rZ\cos\phi)^{1/2}}.

    If we assume Z>r this integral is easy and gives the formula above.

    I hope this is what you're after.
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