- #1
tellmesomething
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- Homework Statement
- An early model for an atom considered it to have a positively charged points nucleus of charge Ze, surrounded by a uniform density if negative charge up to radius R. The atom as a whole is neutrality. For this model, what is the Electric field at a distance r from the nucleus
- Relevant Equations
- None
This is a discussion for (r<R).
Assuming a gaussian surface at x=r from the center we get
$$E(r) = \frac{Ze} {4π\epsilon_0} ( \frac{1} {r²} - \frac{r} {R^3} )$$
However we get the same result if we consider a wholly negatively charged solid sphere and find the field at a distance r inside the sphere and add it with the field due to a single point charge kept at the centre of such a sphere...
$$E(r)=E_{-ve sphere}+E_{+ve point charge}$$
How can we consider the field due to the whole negative sphere, isnt the middle albeit being a very small point charge positive instead of negative?
field due to a wholly negatively charged sphere + field due to a point positive charge≠ Field due to a negatively charged sphere with its midpoint being empty+ field due to a point charge
Is this just an approximation? Or do I not know how to apply the superposition principle. Please consider helping out
Assuming a gaussian surface at x=r from the center we get
$$E(r) = \frac{Ze} {4π\epsilon_0} ( \frac{1} {r²} - \frac{r} {R^3} )$$
However we get the same result if we consider a wholly negatively charged solid sphere and find the field at a distance r inside the sphere and add it with the field due to a single point charge kept at the centre of such a sphere...
$$E(r)=E_{-ve sphere}+E_{+ve point charge}$$
How can we consider the field due to the whole negative sphere, isnt the middle albeit being a very small point charge positive instead of negative?
field due to a wholly negatively charged sphere + field due to a point positive charge≠ Field due to a negatively charged sphere with its midpoint being empty+ field due to a point charge
Is this just an approximation? Or do I not know how to apply the superposition principle. Please consider helping out
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