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deedsy
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Homework Statement
A spherical charge distribution is given by [itex] p = p_0 (1- \frac{r^2}{a^2}), r\leq a[/itex] and [itex] p = 0, r \gt a [/itex], where a is the radius of the sphere.
Find the electric field intensity inside the charge distribution.
Well I thought I found the answer until I looked at the back of the book...
Homework Equations
[itex] \oint \vec E \cdot d \vec A = \frac{q_{inside}}{\epsilon_0}[/itex]
The Attempt at a Solution
[itex] \oint \vec E \cdot d \vec A = \frac{q_{inside}}{\epsilon_0}[/itex]
[itex] E 4\pi r^2 = \frac{4\pi r^3 p}{3 \epsilon_0}[/itex]
[itex] E = \frac{p_0 r}{3\epsilon_0}(1 - \frac{r^2}{a^2}) [/itex]
but my book has as the answer:
[itex] E = \frac{p_0 r}{\epsilon_0}(\frac{1}{3} - \frac{r^2}{5a^2}) [/itex]
I have no idea where the extra factor came from... Did I do something wrong or is it a mis-print?