# Dipole moment of electrically neutral system of charges.

**Electricity and Magnetism**Level 4

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).