Consider the electric field
\begin{equation}
\vec E(r,\theta,\phi) =
\begin{cases}
0&\textrm{for } r<a\\
\frac{1}{4\pi\epsilon_0} \,\frac{Q}{b^3-a^3}\,
\left( r-\frac{a^3}{r^2}\right)\, \hat r & \textrm{for } a<r<b\\
0 & \textrm{for } r>b \\
\end{cases}
\end{equation}
- Use step and/or delta functions to write this electric field as a single
expression valid everywhere in space.
- Find a formula for the charge density that creates this electric field.
- Interpret your formula for the charge density, i.e. explain briefly in words where the charge is.