Question 2.12: Use Gauss’s law to find the electric field inside a uniforml...

Introduction to Electrodynamics – Solution Manuals [EXP-2863]

Use Gauss’s law to find the electric field inside a uniformly charged solid sphere (charge density ρ). Compare your answer to Prob. 2.8.

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$\oint{}E\cdot da = E · 4\pi r^2=\frac{1}{\varepsilon _0} Q_{enc}=\frac{1}{\varepsilon _0}\frac{4}{3} \pi r^3\rho$ . So

$E=\frac{1}{3\varepsilon_0 } \rho r\hat{r}$ .

Since $Q_{tot} =\frac{4}{3}\pi R^3\rho ,E=\frac{1}{4\pi \varepsilon _0}\frac{Q}{R^3}\hat{r}$ (as in Prob. 2.8).

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