# Electric dipole moment, which charge is the $q$ for?

Electric dipole moment says $p = qd$. Which charge does the $q$ equal to?

• You book no doubt sets this up with a particular situation. Look back at how they defined it... – dmckee --- ex-moderator kitten May 22 '13 at 20:54

## 1 Answer

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 but opposite charge $q$ and $-q$. In this case $\mathbf{ d}$ has magnitude $qd$, where $d$ is the charges' relative separation, and points from the $-$ charge to the $+$ one. If there are more charges you need to apply the general formula.

It is worth mentioning that for a neutral system the dipole moment is independent of the origin, but for a charged system it does matter where the origin is (and at the "center of charge" it is zero). See e.g. this question.

• Does it really make sense to talk about the dipole moment of a single charge? – Groda.eu May 23 '13 at 18:29
• Yes. You can always define it, of course, and it is useful in that it gives the subleading term of the multipole expansion of that charge's field when it is displaced from the origin. – Emilio Pisanty May 23 '13 at 18:34