Dipole moment of electrically neutral system of charges.

The dipole moment for a system of charges is defined as $\vec{d}=\sum_{k} q_{k} \vec{r}_{k}.$ (see here for a more in depth discussion of the dipole moment). Determine the magnitude of the dipole moment in $$\mbox{m} \cdot \mbox{C}$$ for a system of three charges ($$Q=1~\mu \mbox{C}$$, $$Q=1~\mu \mbox{C}$$, and $$-2Q=-2~\mu \mbox{C}$$) located on the vertices of an equilateral triangle of side $$a=1~\mu \mbox{m}.$$ One can show that for an electrically neutral system, the dipole moment is independent of the origin of coordinates (which makes this problem unambiguous).

×