Remark on Dipole-Dipole Interaction

The interaction energy of two dipoles with distance vector ${\bf R}$,

$$E^{\rm d-d}({\bf R}) = \frac{{\bf d}_1 {\bf d}_{2}}{\vert{\bf R}\vert^3}-3 \frac{({\bf R} {\bf d}_1) ({\bf R}{\bf d}_{2}) }{\vert{\bf R}\vert^5}$$ (2.8)

can alternatively be written as

$$E^{\rm d-d}({\bf R}) = -{\bf d}_1{\bf E}^{\rm dip}_2 = -{\bf d}_2{\bf E}^{\rm dip}_1,$$ (2.9)

where ${\bf E}^{\rm dip}_2$ is the electric field generated by dipole $2$ at the position of dipole $1$, and vice versa.