Question: Consider a constant electric dipole moment (mathbf{p}) at the origin. It produces an electric potential of (phi=frac{boldsymbol{p} cdot mathbf{r}}{4 pi epsilon_{0} r^{3}}) outside the dipole.

Consider a constant electric dipole moment $\mathbf{p}$ at the origin. It produces an electric potential of $\phi=\frac{\boldsymbol{p} \cdot \mathbf{r}}{4 \pi \epsilon_{0} r^{3}}$ outside the dipole. Noting that $\mathbf{E}=-abla \phi$, find the electric field at $\mathbf{r}$.

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