- 383

- 13

- Homework Statement
- Given a spherical shell of radius R and charge density ##\sigma_0##, find the electric field at point A r<R and point B r>R using the superposition principle. With this results, find the analogous problem with a solid sphere with charge density ##\rho_0##

- Homework Equations
- ##\vec E=\frac{1}{4\pi\epsilon_0}\int \frac{\sigma}{r^2}\hat{r}##

Hi! I need help with this problem. I tried to solve it by saying that it would be the same as the field of a the spherical shell alone plus the field of a point charge -q at A or B. For the field of the spherical shell I got ##E_1=\frac{q}{a\pi\epsilon_0 R^2}=\frac{\sigma}{\epsilon_0}## and for the point charge ##E_2=\frac{-q}{4\pi\epsilon_0 r^2}##, I said that -q was the same as q, and so I could write it as ##E_2=\frac{-\sigma R^2}{\epsilon_0 r^2}##. After thaht I add them and I got ##E=\frac{\sigma}{\epsilon_0}[1-\frac{R^2}{r^2}]##. As I understand, I was meant to get ##E=0##, since at A r<R. what am I doing wrong?