It is the difference in distance between the molecules centre of gravity/mass and the centre of gravity of the electron cloud.
YES!! We are talkinf very small distances.
If we take hydrogen chloride as an example. It is structure is H -Cl .
The chlorine atom as a very strong electro-negativity(Pauling Scale) and pulls electrons towards itself. leaving the hydrogen atom denuded of an electron cloud.
Its a bit like the clouds around the Earth, some places the clouds are very dense, other places the clouds are thin and in other places there are no clouds.
Whilst the HCl bond does not break , it leaves the hydrogen with a very thin electron cloud,
Electrons have a duality of character. They can have a dot/point ( Nils Bohr orbitals) , this is the centre of mass. , but also it exists as a cloud.
So for HCl the centre of mass of the molecule will be at a given point , but the centre of mass of the electron cloud will NOT be at the same place, because the electron cloud is thicker/thinner in different places. This is the dip[ole moment.
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