Dipole moment of electrically neutral system of charges.

The dipole moment for a system of charges is defined as d=kqkrk. \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 mC\mbox{m} \cdot \mbox{C} for a system of three charges (Q=1 μCQ=1~\mu \mbox{C}, Q=1 μCQ=1~\mu \mbox{C}, and 2Q=2 μC-2Q=-2~\mu \mbox{C}) located on the vertices of an equilateral triangle of side a=1 μm.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).

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