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## Homework Statement

We have a uniformly charged solid sphere whose radius is R and whose total charge is q. I'm trying to find the electric field inside a (r<R).

The correct answer must be:

[itex]E=\frac{1}{4 \pi \epsilon_0} \frac{q}{R^3} r \hat{r}[/itex]

How did they get that answer?

## The Attempt at a Solution

Since the sphere is not a shell, the E is not 0. And it should be found by considering a concentric Gaussian sphere with radius smaller than R. So by using Gauss's law for electric fields in the integral form we obtain:

[itex]\oint E . da = E \oint da = E (4 \pi r^2) = \frac{q}{\epsilon_0}[/itex]

[itex]\therefore E = \frac{q}{4 \pi \epsilon_0 r^2}[/itex]

For E outside the sphere we use r>R, and inside the sphere we use r<R. But why is my answer so different from the correct result?

Any help is greatly appreciated.