What is electric dipole?

I don't understand the electric dipole as it is described in my physics book. According to what I have read in my chemistry book, I know that the dipole is the gain of partially negative charge in the electronegative end and vice versa. This results in a type of weak Van der Waal force. However, in physics I don't find the same explanation. In physics, it is described as the product of the magnitude of charge, $q$, and distance between the two equal and opposite charges, $\textbf{d}$. How can both of these definitions be the same?

The dipole moment is uniquely defined as $$\vec{\mu}=\sum_i^N q_i \vec{r}_i$$ Unfortunately in Chemistry, when the molecular dipole moment is represented, that is done as an arrow with a cross in the tail pointing from the positive charges to the negative ones. The reason why this convention is so common in Chemistry is because it reflects atomic electronegativities: for example the oxygen being more electronegative than hydrogens "pulls" electrons towards itself, leading to the partial charges represented with $\delta^{+}$ and $\delta^{-}$. On the other hand the formal definition of a dipole moment (the one given above) is represented by the following vector representation