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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?

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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.Chemical representation of water dipole moment as sum of bond dipoles 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

Dipole moment represented using the formal definition

To sum up the dipole moment is a vector uniquely defined that contains information about the charge separation. However in Chemistry it can be represented in the opposite way (only represented: when we (chemists) do calculations we of course use the formal definition). In practice the molecular dipole moment is obtained integrating the electron density since we have a charge distribution all over the space and not fixed partial charges, thus it is an expectation value of the molecular wavefunction. There is no need to invoke Van der Waals interactions for defining the dipole moment!

I really hope it helps! :)

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I'm not very familiar with the chemical term, but they do sound like they are the same.

An electric dipole is an object (or, in general, a charge distribution), where the two charges are not evenly distributed. Imagine a convenient object for starts, like a rod. The positive and negative charges could be completely separated spatially, or they could be mixed but unevenly. You have an electric dipole in both cases, and its moment is stronger in the first case. (You can see that it is stronger from, as you said, the product of the magnitude of charge and distance.)

"The gain of partially negative charge in the electronegative end and vice versa" sounds like such a case. The van der Waals would be a result of this configuration.

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