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Hydrogen bonds do have dipole moments because they typically form when a hydrogen atom bonds to a highly electronegative atom (F,O,N). When bonded to these specific highly electronegative atoms, the hydrogen bonds will have a dipole moment.
As stated before, hydrogen bonds do have dipole moments due to the difference in electronegativity between hydrogen and electronegative atoms like nitrogen, oxygen, and fluorine. This also makes sense because molecules can involve multiple intermolecular forces. In a molecule with hydrogen bonds, dipole-dipole interactions as well as induced dipole-induced dipole interactions can occur.
The dipole moments in hydrogen bonds are also what allows various hydrogen-bond molecules to interact with each other (as is the case in water). The dipole moment creates partial charges that attract the partial charges of other molecules.
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