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The dipole moment of a system of charges $q_i$ located at positions $\mathbf r_i$ is defined as the vector $$\mathbf d=\sum_i q_i\mathbf r_i.$$ If you have a single charge $q$ at $\mathbf r=d\hat{\mathbf e}$ then $\mathbf{d}$ has magnitude $qd$ and points along the unit vector $\hat{\mathbf e}$. Usually, however, this is introduced for two charges of equal ...

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