2) (20 points) The electrostatic potential of an electric dipole $\vec{p}$ located at the origin is $\phi(\vec{r}) = \vec{p} \cdot \vec{r}/r^3$. Here, $\vec{p}$ is a constant vector and $r = \sqrt{x^2 + y^2 + z^2}$. Write $\phi$ in Cartesian coordinates and calculate $\partial\phi/\partial x$, the x-component of the gradient. Use this to obtain $-\nabla\phi$ (the electric field). Write the result in terms of $\vec{p}$, $\vec{r}$, and r.