Module 2 : Electrostatics
Lecture 10 : GAUSS'S LAW
 

The field outside the sphere is what it would be if all the charge is concentrated at the origin of the sphere.
For $r <R$, a fraction $r^3/R^3$of the total charge is enclosed within the gaussian surface, so that

\begin{displaymath}4\pi r^2 \mid E\mid =\frac{1}{\epsilon_0} \frac{Qr^3}{R^3}\end{displaymath}

The field inside is

\begin{displaymath}\vec E = \frac{Q}{4\pi\epsilon_0}\frac{r}{R^3}\hat r\end{displaymath}
  Exercise 1
  Exercise 2
  Exercise 3
  Example 7
  Exercise 4
  Exercise 5
  Example 8
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