Up to this point I know that two equal and opposite electric charge constitute an electric dipole. But when I study the "Introduction to electrodynamics" by DJ Griffiths, the author a consider a single charge as an electric dipole which is at a distant $d$ from the origin. Now in what sense a single electric charge can be considered an electric dipole and What is correct definition of electric dipole?
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$\begingroup$ Can you please point out the page/section of the book where this is mentioned? $\endgroup$– Amey JoshiCommented Nov 6, 2019 at 1:32
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$\begingroup$ In Radiation chapter. Page no 457, example 2 $\endgroup$– no oneCommented Nov 6, 2019 at 13:14
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Dipole moment $p$ is defined to be $$p=\sum_{i} q_i\vec{r_i}$$ where $q_i$ is the charge, and $r_i$ are the charge and position vector measured of the ith particle measured from the origin. So dipole moment is a perfectly well-defined quantity even if there is only one charge. If you happen to choose the origin of your coordinate to be where the one charge is, then the system has zero dipole moment. Otherwise, it has nonzero dipole moment.
In general, the dipole moment of a system is dependent on the choice of origin of your coordinates. Only if the total charge of the system is zero, the the dipole moment is the same regardless of where you choose the origin (try to show it yourself!)
