Module 2 : Electrostatics
Lecture 7 : GAUSS'S LAW

The charge enclosed by the gaussian surface is

\begin{eqnarray*} Q &=& \int_0^r\rho(r) d^3r = \int_0^r \rho(r) 4\pi r^2 dr\\ &=& 4\pi k\int_0^r r^3dr\\ &=& \pi k r^4 \end{eqnarray*}

Thus

\begin{displaymath}\vec E = \frac{1}{\epsilon_0}\frac{kr^2}{4}\hat r\end{displaymath}

(what is the dimension of $k$?)

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