3.2: Mathematical Definition of Dipole Moment
- Page ID
- 5425
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In the introductory section 3.1 we gave a physical definition of dipole moment. I am now about to give a mathematical definition.
\(\text{FIGURE III.2}\)
Consider a set of charges \(Q_1, Q_2, Q_3 ...\) whose position vectors with respect to a point \(O\) are \(\textbf{r}_1\), \(\textbf{r}_2\), \(\textbf{r}_3\)... with respect to some point O. The vector sum
\[ \textbf{p} = \sum_i Q_i \textbf{r}_i\]
is the dipole moment of the system of charges with respect to the point O. You can see immediately that the SI unit has to be C m.