This problem rotates about electric fields created by charges.

Gauss law:

$\overline{){{\mathbf{\varphi}}}_{{\mathbf{E}}}{\mathbf{=}}{\mathbf{\int}}{\mathbf{E}}{\mathbf{\xb7}}{\mathbf{dA}}{\mathbf{=}}\frac{{\mathbf{Q}}_{\mathbf{e}\mathbf{n}\mathbf{c}}}{{\mathbf{\epsilon}}_{\mathbf{0}}}}$

The electric field of a uniformly charged non-conducting sphere:

$\overline{){\mathbf{E}}{\mathbf{=}}\frac{{\mathbf{Q}}_{\mathbf{e}\mathbf{n}\mathbf{c}}\mathbf{R}}{\mathbf{4}{\mathbf{\pi \epsilon}}_{\mathbf{0}}{\mathbf{r}}^{\mathbf{3}}}{\mathbf{;}}{\mathbf{}}{\mathbf{R}}{\mathbf{\le}}{\mathbf{r}}\phantom{\rule{0ex}{0ex}}{\mathbf{E}}{\mathbf{=}}\frac{{\mathbf{Q}}_{\mathbf{e}\mathbf{n}\mathbf{c}}}{\mathbf{4}\mathbf{\pi}{\mathbf{\epsilon}}_{\mathbf{0}}{\mathbf{R}}^{\mathbf{2}}}{\mathbf{;}}{\mathbf{}}{\mathbf{r}}{\mathbf{\ge}}{\mathbf{R}}}$ where r is the radius of the sphere and R is a point of interest. This equation is identical with the electric field of a point charge for r ≥ R.

The nuclei of large atoms, such as uranium, with 92 protons, can be modeled as spherically symmetric spheres of charge. The radius of the uranium nucleus is approximately 7.4×10^{−15} m.

a. What is the electric field this nucleus produces just outside its surface?

b. What magnitude of electric field does it produce at the distance of the electrons, which is about 1.7×10^{−10} m?

c. The electrons can be modeled as forming a uniform shell of negative charge. What net electric field do they produce at the location of the nucleus?

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