- #1
ghostfolk
- 59
- 1
Homework Statement
A spherical conductor of radius ##a## carries a charge q and also there is a jelly of constant charge ##rho## per unit volume extending from radius ##a## out to radius ##b##.
I'm looking to see if I got the correct set up for the electric field of this spherical conductor for all space.
Homework Equations
##\oint \vec{E} \cdot d\vec{a}=\frac{Q_{enc}}{\epsilon_0}##
The Attempt at a Solution
##\oint \vec{E} \cdot d\vec{a}=4\pi r^2##
##Q_{enc}=\int_a^r 4\pi r'^2 \rho dr'+q=\frac{4\pi}{3}(r^3-a^3)\rho+q##
So then,
##E=\begin{cases}
0, r<a& \\\
\rho \frac{(r^3-a^3)}{3r^2 \epsilon_0}+ \frac{q}{4\pi r^2\epsilon_0} \hat{r}, a<r<b\\
\rho \frac{(b^3-a^3)}{3r^2 \epsilon_0} +\frac{q}{4\pi r^2\epsilon_0} \hat{r}, b\le r
\end{cases}##